Studies on Sintering and Grain Growth in Magnesium

STUDIES ON

SINTERING AND GRAIN GROWTH

IN MAGNESIUM

CHRISTOPHER PAUL BURDESS, B.Sc.,A.R.C.S.

A Thesis submitted for the Degree of Doctor of Philosophy

in the University of London.

August 1966 Chemistry Department, Imperial College of Science and Technology, LONDON S.W.7. ABSTRACT.

Pure magnesium oxide (1200 ppm metallic impurities) was prepared by calcining pure magnesium oxalate which. had been produced by mixing purified solutions of magnesium nitrate and ammonium oxalate. The hydration characteristics in air atmospheres at different relative humidities were studied in order that the effect on sintering of dehydration might be estimated. The rate of hydration of magnesium oxide is discussed. Infra-red spectrophotometric studies were made in order that the surface conditions might be better known. The sintering of pure magnesia was studied, and found not to obey the semilogarithmic densification law found by other workers. Data for two successive smaller ranges of densification gave two activation energies, comparable however with. those obtained by other workers who applied the semilogarithmic densification laws to the whole range of densification. The grain growth during the sintering of pure magnesium oxide of small initial particle size was found to occur in two stages, at least on the surface, and probably also in the bulk of the material. An initial stage, characterised by growth from nuclei, and obeying a grain size o< time law (probably discontinuous grain' growth), was n followed by normal grain growth, characterised by a (grain size) o< time law, where n is close to 2. Other types of grain groW-th and other effects during. sintering and grain growth were examined microscopically and by electron microprobe analysis. I Dedicate this Thesis to my Grandmother,

Mrs. Mabel Burdess. CONTEUTS

Chapter 1. Introduction and Literature Survey 1

Chapter 2. Experimental Techniques 87

Chapter 3. Pure Magnesium Oxide 102

Cha:oter 4. Sintering 151

Chapter 5. Grain Growth 177

Chapter 6. Discussion 214

References 233

Acknowledgements 246

CHAPTER 1.

Introduction and Literature Survey. 1.1. Introduction 2 1.2. Sintering - Phenomena and Mechanisms 3 (a) Early Observations on Sintering 3 (b) The VisOoub Flow Model 5 (c) Neck Growth. Relations for Sintering Models 8 (d) Evidence for Diffusion in Microcreep experiments 14. (e) Diffusion in Sintering 14. (f) Sintering Ionic and Covalent Solids 16 (g) Grain Boundaries as Vacancy Sinks 18 (h) Further Treatment of Model Systems 19 (i) Role of Grain Boundaries in Vacancy Annihilation 26 (j) Diffusion Mechanisms and Sintering 28 (k) Diffusion paths in Sintering 29 (1) The Intermediate Stage Sintering Models 36 (m) Further Work on the Sintering of Oxides 39 (n) Revision of the Initial Stage Sintering Model 41 Co) Further Work on the Intermediate Stage of Sintering 43 (p) Recent Work on Diffusion and Sintering in Oxides 49 1.3. The Effect of Additives and Atmospheres on Sintering 51 (a) Introduction 51 (b) The Importance of Solid Solutions 53 (c) Surface Effects and Solid Solutions 54- (d) The Effect of Atmospheres 59 (e) The Effect of Water-vapour on Sintering of Oxides 61 1.4. Hydration of Magnesium Oxide 62 1.5. Grain Growth 66 (a) Introduction and Early Observations 66 (b) The Importance of Crystallographic Orientation 70 (c) The Mechanisms of Grain Growth 71 (d) The Effect of Inclusions 73 (e) Work with. Pure Metals 74 (f) Theoretical Anpects 75 (g) Grain Growth in Non-metals 76 (h) The Effect of Grain Boundaries and Pores on Grain Growth 82

1.6. Broad Conclusions from Previous Work; Fields for Further Research

PO, 85 - 2 -

1.1. INTRODUCTION.

A set of small particles has a greater-free energy than a large particle of the same volume, because of the greater surface energy arising from the surface area difference. Similarly, a particle consisting of numerous crystals of different orientations, separated from each other by grain boundaries, has a greater free energy than a single crystal.

Under appropriate conditions, the small particles may agglomerate and densify to a body of smaller surface area, and the body may further reduce its free energy by conversion to a single crystal. Fass and White (1966) have obtained a single crystal of cadmium sulphide by such a process - sintering a powder compact - but it is more usual for sintered products to contain solid-vapour and solid-solid boundaries (pores and grain boundaries).

Sintering and grain growth occur in the formation of metamorphic rocks: the rocks are eroded to small particles, sedimented in estuaries etc., and pressed at high pressures and heated for long times during g..64.0... logical upheaval. The process may be seen in the review of Voll (1960) on observations- of geological grain growth.

The procesS of sintering with a liquid phase between the particles, in the form of pottery manufacture, has been known for some 5,000 years, but it was not until comparatively recently that the sintering of pure crystalline solids, without a liquid phase being present, was considered possible, and even then, sintering was considered difficult (Crone and McKee, 1950). Liquid phase sintering, afritting", is not considered in detail in this review, and the reader is referred to Jones (1960) and Kingery (1959). 2 The surface energy of magnesium oxide is about 1150 ergs/cm . (Jura and Garland, 1952; Livey and Hurray, 1956; Gilman, 1960; Westwood and Goldheim, 1963). The excess free energy, d G, of a powder of diameter particles is about o.46 cal/g (145 cal per mole) above that of a single crystal, and for 200A particles AG-23cal/g, (920 cal/mole). 3 -

The major proportion of this free energy is available for sintering, in which the small particles change shape and consolidate together so that their surfaces become grain boundaries, and the remainder is available for grain growth, where the total grain boundary area is reduced. The proportions depend on the relative values of the surface and grain boundary energies. While it is easy to separate sintering and grain growth in theory, in practice the two phenomena are related, and grain growth may occur before sintering is complete.

During sintering, material transport may occur by any one or a combination of the following mechanisms:

(1) Viscous or other macroscopic flow, (2) Evaporation-condensation, (3) Volume, grain boundary or surface diffusion, though not all the possible mechanisms have been recognised from the start of work on the theoretical aspects of sintering.

1.2. SINTERING - 1),IIEN0rjalA AND AILHANISMS.

(a) Early Observationsi on Sintering.

An observation by Faraday (1857) that a gold leaf mounted on glass and heated to 500°C lost its green colour and became transparent, reap- pearing on burnishing, was explained by Turner (1908) as a breaking-down of the continuous foil into a network of gold strands, which flatten out somewhat on burnishing. This ability of a material to decrease its surface area at temperatures below the melting point had been used in the process developed in the early 18th century for the consolidation of platinum sponge.

The investigations into the properties of finely-divided noble metal and other catalysts early this century brought interesting observations on sintering.

Wright and Smith (1921) noted the decrease in specific surface which accompanied sintering in the conversion of platinum black to grey - 4 -

and white platinum, and noted that mounting on asbestos preserved the platinum black longer at high temperatures, ascribing this reduction of sintering to the reduced inter-particle contact. The cause of sintering was thought to be the property which also caused increased vapour pressure and solubility of small particles. Smith (1923) considered that any lowering of the melting-point of a substance due to diminution of particle size was unlikely to be more than a fraction of a degree,so the material must certainly be solid at the time of sintering. Polished surfaces were thought at that time to consist of a layer of amorphous material on top of the main crystalline mass, and it was reported that such "amorphous" surfaces sintered more readily than crystalline ones, though the significance of a greater area of contact was recognised. It was also found that fine iron powders sintered most readily at temperatures known to correspond to phase transformations.

Hedvall (1922), in investigations of colour changes on heating iron oxides, noted the spheroidisation of haematite platelets, and the coalescence of small particles into large ones on heating.

Work by Roberts-Austin (1896) on the diffusion of gold in lead, and by Groh and von Hevesy (1920) on the self-diffusion of lead, showed the possibility of diffusion in solids, and the work of Tammann (1921) and Endell (1922) on the growth of reaction layers and on reactions in solid powders showed the applicability of diffusion to solid state reactions.

Sauerwald (1923) suggested a "sintering temperature" of about two-thirds of the absolute me ting-point, but the experiments of Tammann and Mansuri (1923), using a paddle-wheel, driven via a friction clutch, revolving in a drum of powder, did not reveal the "sintering temperature" at which the paddle--wheel stopped as being 5

a significant fraction of the melting-point in the same way as the "Tammann temperature" was held to be significant for diffusion. Muller (1935) showed, in effect, that on isothermal sintering the strength of a rock-salt compact first increased, owing to neck formation between the particles, and then, at longer times, the strength decreased owing to grain growth in the compact.

li Huttig (1942) considered that surface diffusion was responsible for the initial stage of sintering. It was in attempts to verify one or other of the various possible material transport mechanisms that the subsequent theoretical treatments of model systems ensued. 1.2(b) THE VISCOUS FLOW MODEL frenkel (1945) studied the model of two spherical particles sintering together by the viscous flow mechanism. It was proposed that vacancies could migrate under stress to give a flow of material, and that the viscosity coefficient,(1, , of the material was related to the diffusion coefficient, D, by the Stokes-Einstein and Eyring formulae: 1DS S = lattice const. for cubic lattice. 7 ` kT k = Boltzmann const. T = absolute temperature. For two particles, radius a, the neck radius x will grow at a rate 1 given by: e = 3 t = surface tension. 2ra t = time. This formula should be valid for a 0.3, and a is relatively unchanged. In the closing of an isolated pore, the time taken for closure t = 51-37 where r = pore radius, in a solid of zero rigidity. Pines (1946) pointed out that there is a variation in the concentration of vacancies in a crystal at different points, due to different curvatures of the crystal surface above the points. More vacancies are sited under a concave surface than under a convex one, because of the increased ability of a ion below such a surface to evaporate. Material transport may occur under the resulting vacancy concentration gradient. .. 0

Bangham (1947) considered that during sintering particles adhere to each other to broaden the contact angle between them, and that small particles should be more adhesive than larger ones. Shaler and Wulff (1948) considered the various possible material transport mechanisms, and concluded that their work on the sintering of copper agreed with a viscous flow model. At the same time, it was claimed that viscous flow and diffusion mechanisms were identical. The rate of material transport under evaporation-condensation was too slow to account for observed rates. Nabarro (1948) pointed out that there was no force on a vacant lattice site in a homogeneous stress field, so that the previous estimates of deformation rates of solids, calculated on the basis of migration of lattice defects under stress, were inapplicable. The stresses can alter the concentration of defects, which are in thermodynamic equilibrium, and these may flow under this concentration gradient, giving rise to "microcreep" in metals. In application iv of the formulae so derived to the data of Muller (1335) for the sintering of rock-salt compacts, it was shown that the contribution of lattice defects produced an effective viscosity at the melting- point six orders of magnitude higher than the observed value at several hundred degrees below the melting-point. Lukirsky (1945) had observed the rate of formation of crystalline facets on sodium chloride, and Nabarro claimed that the rate was too fast to be attributed to diffusional flow. However, it was also suggested that vacancies might he discharged at mosaic boundaries and grain boundaries as well as the free surface.

Udin, Shaler and Wulff (1949) attempted to deduce the value of the surface tension of solid copper, essential in quantitative application of sintering models. Small weights were hung on fine copper wires, and the strain rate was found to be proportional to the stress. This corresponds to viscous flow, explained by the Nabarro mechanism. The-,10% higher value for the surface tension of copper obtained by Harkins (1942), by calculating the energy of bonds broken in the formation of unit area of new surface, was explained by Udin et al. as possibly due to distortion in the surface layer taking up some energy, a possible explanation for the strengthening of the surface. However, Udin (1951), Funk, Udin and Wulff (1951) and Buttner, Udin and Wulff (1951) calculated the surface tension of copper, silver and gold by obtaining the stress at zero strain and applying a correction for the grain boundaries, which gave a slightly higher value. Kuczynski and Alexander (1949), in the discussion of the paper of Udin et al* (1949) queried the proportionality of stress to strain, considering the scatter of the data. They also derived a diffusion coefficient of D = (5.104)exp(-66000) from the data. The temperature depende= RT was of the same order as previously determined values for the volume diffusion of copper, but the frequency factor was much higher. The possibility of a surface diffusion mechanism was suggested. Jordan and Duwez (1949) sintered copper powder compacts in hydrogen and in 7acuo, and plotted a densification parameteri c-, against log t, where eo= sintered density A= green density = theoretical density. It was claimed that if a given state is obtained after time t 1 at T h, and after time t at o 1 o 2 T2 K.' then the times should be related by ln 112- = activation energy fl 11- R = gas constant. From the vs. log t plots, log t values at constant were taken for various temperatures, and these produced straight parallel 1 lines on a log t vs. -- plot. Activation energies of 128 Kcal/mole for vacuum sintering and 80 Kcal/Mole for hydrogen sintering were obtained.

Geach and Jones (1949) observed that the boundary between two particles being sintered together remained stationary, and the pores between them became rounded. 1.2 (c) NECK GROWTH RELATIONS. FOR SINTERING MODELS.

Kuczynski (1949a)considered the possible mechanisms of material transport during sintering, and used the model of sintering spheres to plates to obtain relations between the neck growth and time. For viscous flow Frenkel's x t relation was noted, and the possibility of plastic flow in which stress is only proportional to strain after a yield point has been reached, was mentioned. For evaporation of the material from the particle surface and deposition on the neck surface, where the vapour pressure is lower, the relation x%ft was derived, assuming the rate-controlling step to be transport of vapour from one surface to the other. In the Case of volume diffusion, Kuczynski assumed that the concentration gradient down which the vacancies flow was LC://) where 2. is the diameter of the neck area, which is the same plane as the line from the centre of the sphere to the centre of the circular neck. is itself inversely proportional to il:. as LC = 5( T6 - -5.) 3 (not 2Y,)r (1;-t)• , as given by Kuczynski), and the particle radius a... • Fick's equation (fluxconcentration gradient).was used, together with formulae relating1', the neck area, and the neck volume, to x and a. The region of vacancy annihilation was not stated, though it was implied to be about f. from the neck surface. There are arithmetical errors in the constant in the formula presented, but these change only the frequency factor of any derived diffusion coefficient, and are probably well within the limits of error in subsequent experiments. The neck-growth relation presented was:

x5 4-0 D t 3 2 - = vacancy volume a k T In considering the possibility of surface diffusion, Kuczynski took the area for diffusion as 2ax6 , 7 = interatomic spacing (though owing, presumably, to a printer's error it is written 2-ri( in the -9

paper), and the concentration gradient and geometrical factors were taken to be the same as before, giving the relation:

x7 56 4 Ds t k T

Thus differentiation between sintering mechanisms was claimed to be possible on the basis of time-dependence of neck growth: 2 Viscous and plastic flow x c;:t Evaporation-condensation Volume (bulk) diffusion x5 't . Surface diffusion x7o(t The volume and surface diffusion coefficients, Dv and Ds, are dependent on temperature according to the relation D = Do exp (- k where D o is the frequency factor, Q is the activation energy for diffusion, R = gas constant, T = Temperature (0K). It may be observed that increasing values of Q give decreasing values of exp(-Q/RT), and a greater dependence on temperature.

Kuczynski studied the sintering of copper and silver spheres to blocks in a hydrogen atmosphere, and also silver spheres to

blocks in air. Plots of log()a vs. log t gave slopes close to 0.2 for all but the smallest (4100 ) particles of copper at lower temperatures (< 600°C.), when a value of about 0.15 was found. Derived values for D gave an activation energy of 56 Kcal/mole v for copper, within the range of values determined by other methods, though the frequency factor was higher, and, for silver, an activation energy (42 Kcal/mole) and frequency factor impressively close to the previously quoted value. Analysis of the presumed surface- diffusion effect at lower temperatures and particle sizes gave less uneqUivocal results, but it was nevertheless assumed that surface diffusion was responsible in that case. Volume diffusion was thus claimed to be the predominant mechanism in neck formation, with increasing control by surface diffusion at lower temperatures and smaller particle sizes. -10-

In discussion of Kuczynski's paper, Shaler and 'Jelin drew attention to the possible difficulties in the determination of mechanisms experimentally, suggested the possibility of plastic flow causing the initial bond, and also pointed out that Kuczynski's analysis did not account for shrinkage.

Dedrick and Gerds (1949) claimed to have confirmed the x5 t relation derived by Kuczynski (1949a) by studying the sintering of single layers of copper particles, with an activation energy of 55 Kcal/mole, but it was pointed out by Holloman (1950) that the data was better represented by an activation energy of 40 Kcal/mole. Dedrick and Gerds (1950) found that a recalculation of their data gave 43 Kcal/mole, fairly close to the lowest published value obtained by other methods. The large range of published values, 44-61 Kcal/mole, for the activation energy of volume self diffusion in copper makes it difficult to prove the volume diffusion coefficient unequivocally by such methods, and it is unfortunate that reliable and consistent values were not available, especially in view of the scatter of points in the plots, which gives a wide ranee of possible activation energies even if the model is obeyed.

Kuczynski (1949b), in studying the sintering of glass, deduced a viscous flow mechanism from a straight-line relationship between 2 x and t in sintering spheres to plates. This mechanism was eon- firmed by later workers, including Kuczynski and Zaplatynskyj (1956) , who studied the rate of closure of capillary glass tubes.

Mackenzie and Shuttleworth (1949) said that sintering could not be accounted for by a diffusion mechanism, because of the excessive time it would take for diffusion to the outside surface of the compact, and that diffusion would lead to densification from the outside inwards, whereas uniform densification throughout the compact is normally observed. (Sintered bodieS are often more porous at the centre than outside, but the effect is never great enough for sintering to be explained only by diffusion to the outside surface). Mackenzie and Shuttleworth ascribed pore shape changes during sintering to diffusion mechanisms, then considered other mechanisms for densification. It was pointed out that viscous flow on Frenkel's model should lead to an identical closure rate for isolated pores as for those in a porous mass, and, to account for observed densification rates, solid copper at 10000C. would have to have a viscosity close to that of treacle at room temperature. As neither of these effects was observed, plastic flow was then considered as a possible mechanism. When a yield point had been reached, flow would occur under which the strain was proportional to the stress above the yield stress. The effective internal negative pressure in pores, due to their surface curvature, would cause high stresses at the pore surfaces, but these would fall off quickly with distance away from a pore, causing no flow into the pore. However, if other pores were sufficiently close to each other to maintain a field of high stress, it was claimed that the yield stress would be exceeded, and flow would occur. Thus both the closure of pores in a porous mass and the stability of isolated pores were accounted for.

Shaler (1949) claimed that metallic particles brought to within a few atomic diameters of each other would experience attractive forces of several thousands of pounds per square inch over the small areas of close proximity owing to the overlap of electron clouds, and that similar large forces had been determined for some non-metals. It was pointed out that surface diffusion and evaporation-condensation could not contribute to densification unless material was transported from the surface to the interior of the compact, and as surface marks on specimens remained visible during sintering, this was clearly not the case. Sintering was thus proposed to occur by an initial cold-weld due to the attractive force, followed by macroscopic flow. For spherical deoxidised x2 copper particles a plot of C2 (----2) vs. t. gave a line which became -12-

straight at higher t values, corresponding to some hours of sintering. The form of flow was thought to be viscous flow, as claimed for the micro-creep experiments on wires, and as the viscous flow was claimed to occur by a diffusion-under-stress mechanism, the activation energy would be the same as for volumn self-diffusion. Clark and White (1950) derived models for the viscous and plastic flow mechanisms for the in#i41 stage of sintering, with the assumption that uniform decrease in particle radius occurred by flow of a thin layer of the surface into the necks. Glass sintered by a viscous flow mechanism, the derived viscosity coefficient agreeing well with values obtained by other methods, and experimentally determined shrinkage rates of alumina, magnesia, and chromic oxide were found to fit derived curves by assuming plastic flow with a yield point decreasing with temperature. This work was extended to calcium oxide, haematite, dolomite and copper by Clark, Cannon and White (1953). At low shrinkages, the data fitted the mechanism of Clark and White (1950), and at higher shrinkages, the Mackenzie-Shuttleworth relations were obeyed. However, while a single activation energy could be obtained for glass sintering, the temperature dependence for the sintering of crystalline solids was not describable by using less than two activation energies. In alumina and magnesia an increase in strength was noted at the temperature at which adsorbed water was released, and it was suggested that hydrogen or hydroxyl bonding was replaced by ionic bonds. This temperature is considerably lower than that at which densification begins.

Herring (1950a) investigated the theoretical aspects of the effect of particle size on sintering. For two sets of particles of radii a respectively, where a the time to reach 2' a1 2 11 an identical extent of sintering, i.e. equivalent -a ratios, for the two sets would be t2 =A1.- The values of n were determined - 13 -

for the various mechanisms of sintering as follows: Viscous flow n = 1 Evaporation-condensation n = 2 Volume diffusion n = 3 Surface diffusion n = It was pointed out that the assumptions made for the viscous flow mechanism were not applicable to crystalline solids, and thus the relation would not be expected to hold for them. For evaporation- condensation it was assumed that the mean free path of a vapour molecule was long compared with the dimensions of the particle, and that the process was controlled by the transport rate between the evaporating surface and the condensing surface. For volume diffusion, it was noted that the chemical potential, fk at the surface of a solid must be equal to the chemical potential in the vapour in equilibrium with the surface. This leads to 1 2 = 5,7. Though it had already. been stated that the flux is proportional to the local chemical potential gradient, it was claimed that flux2 - 1114x1;. 9 indicating that the vacancy concentration gradient was independent of 2 particle size. The areas for diffusion are in the ratio X and the volumes to be filled in the ratio X:3, thus the amount filled in unit time would be in the ratio V = V. or t = ),3t . Similarly, 2 ,W1, 2 1 in surface diffusion, Herring assumed that fluX2 = flux1, with the diffusion taking place across a length in'the plane of the Surface,_ normal to the flux direction.. which would than give: .= -a- V , or t = .X.3t . 2 A>3 1 2 1 J_2 As Horring derived t A' t =X3t for volume diffusion, -A_2 1 1 and t = ) 2 = Xt4 for Surface diffusion, it will be seen that 2 3A. t1 1 the inconsistency in-his calculations was that while claiming that flux2 = fluxi the relation flux2 = fluxi had been used. It appears that the assumption made by Kuczynski (1949q was used, i.e the vacancy concentration gradient v C (where- r0A)-)2c—a and .Cy-'-,1 I?1, .

C 2a 2a = a 21 Thus ----2( 2 12(X)4 (—x ) ' which, for identical 3z 2 a flux x x 1 extents of sintering (identical values of a gives flux2 = 2 Thus it cannot be claimed that Herring (1950a) confirmed the findings of Kuczynski (1949a),as the same assumptions were used.

1.2(d). EVIDENCE FOR DIFFUSION IN MICROCREEP EXPERIMENTS.

In a paper on the theoretical aspects of microcreep in wires, Herring (1950b) discussed the vacancy annihilation sites suggested by Nabarro (1948), and considered that mosaic boundaries and low- angle grain boundaries were unlikely to absorb vacancies, but higher- angle grain boundaries and the free surface would be able to do so. The derived viscosity coefficient in microcreep should obey the D relation 1 v R = radius of wire RLT L = length of wire. if microcreep occurred by diffusion of vacancies from grain boundaries under tension to those under compressive stress. This would lengthen and thin out the wire. It was pointed out that it could not be concluded that single crystals would not creep, indeed, Miller (1936) had shown that zinc single crystals creep very fast even under 2 stresses of only 2-3 g/mm . However, Greenough (1952) showed that single crystal silver wires deformed at a rate 10-50 times less than that for poly-crystalline wires. Thus, though slip and kinking contribute to creep, the "Nabarro-Herring" mechanism is predominant. It is reported that Foiweiler (1961) successfully applied the microcreep relation to the creep of dense polycrystalline alumina, and a diffusion coefficient was derived which agreed well with the diffusion coefficients obtained by Coble (1961) for the later stages of sintering.

1.2(e) DIFFUSION IN SINTERING.

The surface diffusion calculations of Kuczynski (1949a) were questioned by Cabrera (1950), who claimed that the characteristic -15-

diffusion distance, which had been taken as p by Kuczynski (4.1-), was difficult to evaluate, but appeared to be a fraction of a, rather a than of ) This led to revision of the time-dependence of neck x2 e size on sintering to x c t for surface diffusion, which made differentiation between volume and surface diffusion on the basis of time depen- deride of neck growth impossible. However, differentiation might be made on the basis of the different activation energies for surface and volume diffusion. The model in the case of surface diffusion was further discussed 5 by Schwed (1951), who derived the relations x oe t for larger particles, and x50( t for smaller particles, the change in time-dependence occurring is the relaxation asp becomes greater or less than C.-F- where is time for the supply of adsorbed molecules to the surface. It was proposed that differentiation might be obtained by experiments on small particles. Kuczynski (1950) considered that in the previous work on the sintering of silver spheres to plates, though it gave a sintering diffusion coefficient, D = 0.60 exp (-42000/RT), close to the volume diffusion coefficient D = 0.89 exp (-45900/RT) obtained by Johnson (1941), the scatter of the data was sufficient to throw doubt on the accuracy of the determination. Silver wire wound round a o mandrel was sintered at temperatures of 460-900 C. in various atmospheres, and for various times. The sintering relation:

x5 D t a2 = 3kT Ir was calculated, using the same assumptions as before. It was confirmed that a plot of log (-3a1) vs. log t gave a straight line of slope ---; values of D were obtained for each temperature, and "a lnDvs. plot gave D = 0.9 exp (-45700/RT), in excellent agreement with Johnson (1941). - 16 -

Similarly, Cohen and Kuczynski (1950), by sintering copper wire, obtained a diffusion coefficient comparable with previous results.

Pi Huttig (1950) considered that adhesion, surface diffusion and volume diffusion provided the major contribution to sintering, and Roberts (1950), though considering the attractive force calculated by Shaler (1949) as too large to be plausible, suggested that an attractive force might dreate stresses when the surface touched, and these stresses could be alleviated by viscous or plastic flow. Volume diffusion would give rise to sintering if the vacancies diffused from the interior to the exterior of the specimen.

The full acceptance of the diffusion model in sintering was hindered by a lack of realisation of the significance of the grain boundary as a vacancy sink, without which it was difficult to imagine the absorption of vacancies inside the sintered material itself. Various observations had been made which were of great significance. Hoffmann and Turnbull (1951) noted that radioactive silver diffused much faster into the grain boundaries from the surface of a silver block than into the bulk of the metal, and Rosi and Alexander (1950) also reported preferential migration of silver at grain boundaries. Achter and Smoluchowski (1951) reported that the rate of penetration of silver into copper at grain boundaries increases as the orientation difference between the two grains increases. Alexander and Balluffi (1950) had noted that in the final stages of sintering, when the porosity was in the form of isolated pores, the pores only continued to shrink while they were intersected by, or at least very close to, grain boundaries.

1.2(f) SINTERING OF IONIC AND COVALENT SOLIDS.

Observations of other factors in sintering were also reported. .The difficulty of sintering covalent materials was illustrated by - 17 -

Geach (1953), who found that germanium did not sinter at 850°C. (m.p. 958°C.). Geach also reported that unoxidised zinc, obtained by filing the metal under carbon tetrachloride, was more sinterable than zinc filed in air. The very much lower sinterability of more covalently-bonded materials, except at temperatures at which phase changes occur, has been reported, though some adhesion has been noted. Thus, Smart and Ellwood (1958) found o that tin powder sintered at 12 C. below the melting point to a rather friable massi and Dietz and Shulle (1963) reported that fine quartz powder started to sinter at 1250°C., and cristobalite sintered at above 1450°C. The importance of phase transformations was shown by Chaklader and Roberts (1959, 1960), who reported that quartz sintered at the quartz-cristobalite transformation temperature with the formation of an apparently amorphous material at the neck. Sintering apparently ceased when the phase transformation was complete. A similar sintering enhancement effect may be observed in the reports of Sauerwald (1922) and Smith (1923) on the sintering of iron, and the work of Duwez (1951) indicated that at the inversion temperature of iron (816°C.), the densification rate was a thousand times greater than at 982°C.

Norton et al. (1953) investigated the sintering of large particles (50-200,) of alumina and zirconium dioxidJ, and found adhesion but no shrinkage on heating to above 2000 C.

Allison and Murray (1954) used a dilatometer to determine the shrinkage rates of sodium fluoride and calcium fluoride, and found limiting densities for each temperature, and these limiting densities were themselves dependent on the original particle size and the compaction pressure. Good correlation was found with the Clark-White mechanism at the initial stage of sintering, and with theMsckenzie-Shuttleworth theory at the closed-pore stage, and thus a plastic flow mechanism was deduced. Measurements of certain physical properties appeared to confirm this view, but it should be noted that the effect of compacting pressure was the opposite of that expected. Gray (1954) considered the low temperature sintering of zinc oxide to be due to some surface property. In density vs. time plots definite end-points were reached, attributed to a flow mechanism, but it was also noted that a film of zinc appeared in the cold-trap when the zinc oxide was heated to o -6 200-250 C. in vacuo (10 mm.Hg). The oxide, which was pale cream owing to its low-temperature preparation, turned gray on heating to 400-500°C. in low partial pressures of oxygen, becoming white at high temperatures. It may be deduced that the interstitial excess of zinc possibly enhanced a vacancy diffusion mechanism.

1.2(g) GRAIN BOUNDARIES AS VACANCY SINKS.

The Kirkendall effect is the formation of large numbers of vacancies in brass by heating to a temperature such that the zinc evaporates out faster than the copper can diffuse in to take its place. Balluffi and Seigle.(1955) noted that while the vacancies normally coalesced into pores, no pores were found near grain boundaries, and shrinkage occurred, indicating that the vacancies are absorbed at the grain boundaries, with the two sides of the boundary coming together to fill in the space, rather than diffusion of vacancies along the grain boundary to be finally discharged at the external surface. In thick specimens, shrinkage did not occur to the same extent, and some elongated pores formed along the grain boundaries,owing to the inhomogeneity of the system.

Seigle and Pranatis (1955) arranged markers at the surface of wires being sintered together, and noted that the markers stayed in place while material filled in the pores, and this movement of material past the markers could be accounted for only by a diffusion - 19 -

mechanism, as a macroscopic flow mechanism would have led to a destruction of the circular arrays of markers. Possibly owing to the provision of a vacancy sink by the markers themselves, there was some variation observed from the anticipated behaviour, but the work nevertheless provided impressive evidence for the diffusion mechanism. Pranatis and Pound (1955) confirmed the relation derived by Herring (1950b) for microcreep in polycrystalline copper wires, and found the detectable creep in single crystal copper wires.

Wilder and Fitzsimmons (1955) found that sintering was enhanced by the use of finer powders, but were unable to deduce a mechanism by use of Herring's "scaling laws", because of the uncertainty of the average particle size. The index of the proportionality constant varied from one to five according to the value of the proportionality constant taken. It was confirmed that loose powders do sinter, contrary to a recurrent suggestion that strain energy introduced in pressing operationgs was responsible for sintering.

1.2(h) FURTHER TREATMENT OF MODEL SYSTEMS.

An important contribution was made by the theoretical and experimental investigations of Kingery and Berg (1955). The model used was of the sintering of two spherical particles. For the 2 Sat neck growth during viscous flow, the expression S3 -= a 2/1 derived by Frenkel (1945), was accepted, and for evaporation- condensation, the relation x3 = K t (K = const.) was derived. a The main difficulty in deriving an expresSion for sintering by a diffusion mechanism was in ascertaining the actual diffusion path. It was taken that the vacancies diffused away from the neck area with circular symmetry, with the bottom of the vacancy concentration gradient at a distance a (= particle radius) from the neck surface.

-20-

5 x 10-pr.5D t For a non-shrinking compact, the relation --7. = v was a4_ ink-),r, kT derived. On the basis that in the region of measurement in(PP ) 4, the relation was then simplified to x5 2.5 TO S3Dvt . - a kT For vacancy diffusion from the neck through the bulk to the surface of the spheres, assuming the spheres to be large enough for their surfaces to be treated as flat, an analytical solution was not obtained, but a graphical solution EaVe the relation: x5 4-0 3D t .

a kT For vacancy diffusion from the neck, through the bulk to a grain boundary sink, possibly involving dislocation climb as the vacancy annihilation mechanism, it was proposed that the flux equation for a surface sink almost applied, and the relation: 5 D t x 80` J3 was given. 2 a -77a -7 These findings are in agreement with the deductions for the sphere-plate model given by Kuczynski (1949a).

The initial volume shrinkage rate for a viscous flow mechanism • 2 was -xpressed as Alr K t and this relation was expected to V = - 2 o a be valid up to 2 vol7;6 shrinkage, and to fail completely by 6 vol-% shrinkage.

The rate of volume shrinkage accompanying vacancy diffusion from the neck to the surface was derived, though consideration of the geometrical aspects shows that no shrinkage will occur unless material is transported from the exterior of the specimen in this case. It can be seen that shrinkage can otherwise occur only if material is transported from inside the particles, or from the grain boundary between two particles. This involves the annihilation of vacancies inside the particles, e.g. by dislocation climb, or at the grain boundaries, and transport of vacancies to the surface of the particles will only change the shape of the pores. The shrinkage relation quoted wast /11r _ 3n .1 ko .13D 14/5 4/5 v 3 t - 21 - 3 j 4/5 AV tL 1sT, n D t 4/5 and as 71- for small shrinkages, r = - r--73-- vi a kT j where n is the number of contacts with other particles, per particle. The same limits as for the viscous flow relation were expected. The shrinkage rate for vacancy diffusion to, and annihilation at, 2/5 25 grain boundaries was also presented: / r 20 o t , while T o iffekT the volume shrinkage rate for the same mechanism was given as: tV 8o lc 3D1 4/5t4/5 V o Experimental investigations of the sintering of glass, by observing the neck growth of glass particles heated on a filament, gave (--)tx t 1 /2.1 a with a derived value for the viscosity coefficient in order-of-magnitude agreement with previously determined values. Kingery and Berg found that sodium chloride spheres exhibited neck growth without shrinkage, rendering the spheres elliptical, and the inverse time exponent, 3.1 ± 0.3, indicated an evaporation- condensation mechanism, which was confirmed by comparison of the derived vapour pressure with known values. The actual value of the vapour pressure was higher than expected by a factor of two, but the temperature dependence agreed with previously determined values. The evaporation-condensation mechanism for sodium chloride sintering has been confirmed by Moser and Whitmore (1960), who found that the rate was controlled by diffusion through a thin boundary layer adjacent to the surface, and by Rozner and Kuczynski (1962), who found that necks formed during sintering of magnesium oxide spheres to sodium chloride plates consisted of normal crystalline solium chloride deposited by evaporation-condensation.

For copper, Kingery and Berg confirmed a diffusion mechanism by showing an inverse time exponent of 5.0-5.5 for neck growth up to more than! = 0.3. The time exponent for linear shrinkage -22-

, was found to be within -930 of 0.4 for linear shrinkage up to 2%. AV The volume shrinkage equation — = k t was shown to'fit the Vo / sintering data for copper given by Clark et al. (1953) up to = 0.06. 0 It was suggested that in view of the findings of Alexander and Ralluffi (1950) and Greenough (1952), grain boundaries probably acted as the major vacancy sink, and dislocations in the bulk played not more than a very minor role.

In studies on the sintering of alumina and zirconium oxide sp#eres 50-1500, in diameter, Kingery and Berg showed that adherence occurred at about 1300°C., and that rapid neck growth occurred then only a slow further increase was noted. There to a were wide differences in neck growth values at different contact points in the same set of spheres. Material of a somewhat different purity content showed rapid neck growth to 2E -,0.12, then no a further sintering, even at 2020°C. for alumina and 2200°C. for zirconia. While pressed compacts showed linear shrinkages up to ev23% on sintering, loose masses of the same alumina material (particle size 50-100kk) showed no shrinkage on heating to the same temperature. It was thought that strain energy introduced by pressing enhanced the sintering rate, though no fracture was observed at points of contact.

Walker (1955) discussed previous work, and drew attention to the possible effects of compacting pressure on sintering. Among these effects are the possible increase in surface area (and hence free energy) by breaking up particles, the introduction of stored strain energy, and the increase in inter-particle areas of contact. The area of contact depends on the size and shape of the particles, the relative orientation, and the particle size distribution. The possible effects of atmospheres and impurities in enhancing sintering were discussed. - 23 -

Bockstiegel (1956) considered that the contact surfaces between two particles sintering together could be approximated to parabolic shells of the same degree, , if not too much sintering had occurred. Using the same assumption as Kuczynski (1949a), 1 1 that the flux was proportional to — (as tICA7 and Tz-;,<1.7), and it /c" dx iconst. . For spherical was taken that the rate of neck growth dt - /D2 particles (',:= 2)J--x_ 2 , and thus 31; , as found by Kuczynski 2a. •L a (1949a) and Kingery and Berg (1955), but for a third degree para- 1 3 7 Therefore, though there boloid (== 3),;)0(x , and thus x t'

a a is the same particle-size dependence for neck growth, the time exponent is reduced from 0.2 to 0.143. For other sintering dx 1 mechanisms dt 7 6pw , where ;B = 1 for evaporation-condensation, and t.:%= i for viscous flow.

For shrinkage of the two particles with parabolic contacts, Bockstiegel derived the relation between shrinkage, Si and time, t, at constant geometry as .)? _ S = Kam. t for volume diffusion, and corresponding relations:

S = t for viscous flow and: 03 S = for evaporation-condensation (though it has been explained above that evaporation-condensation cannot give rise to shrinkage in a compact, it can give rise to union of two particles, at least in theory). The time exponents for shrinkage and neck growth are given in Table 1.1 for spherical particles (c= 2) and for particles whose contacting surfaces are of parabolic degree c--;.= 3.

- 24 -

TABLE 1.1 TIME EXPONENTS FOR SHRINKAGE AND NECK GROWTH.

Time exponent for: . Shrinkage Neck growth Mechanism 2 3 : 2 \---7.=______3 Viscous flow - 1.00 1.20 0.50 0.40

Evaporation-Condensation 0.66 0.75 0.33 0.25

Volume diffusion 0.4o 0.43 0.20 0.14

- - •

Fig. 1.1. shows how small the difference in shape is between a paraboloid ofq. 3 and a sphere, close to the point of contact.

FiG.I.( of a 6441.111l,gi(ppOnuous line). a nd -a PARABOLOID (broken line).

Thus it appears that small changes in the geometry of a system undergoing sintering can have a much greater effect than was anticipated on the relations for neck growth and shrinkage. Kuczynski (1956) considered that only grain boundary diffusion of vacancies, and volume diffusion of vacancies to grain boundary sinks, could be responsible for shrinkage. For grain boundary diffusion, assuming diffusion of vacancies to the surface via grain boundaries, the rate of closure of isolated pores was 4 4 21(. 6LE given as r r o k T Db t, if the boundary were one atomic diameter thick. A ratio D :D of about 103 v :1 was used to derive -25-

the time for closure of a pore in copper (r . 10-3 cm.) of 5 o about 2.5 x 10 hours, which is much longer than is found in practice.

Volume diffusion to a grain-boundary sink, from whence the vacancies diffused to a surface where they could be annihilated (considered by Kuczynski to be a solid-vapour surface), was considered. The actual position and method of annihilation is not relevant to the calculations if the volume diffusion step is rate-controlling. It was taken that the vacancy concentration , gradient LC, where r is '6x the pore radius. There may thus be a single pore, or an array of pores, but no difference to the treatment is made unless the pores are separated only by distances of the order of the characteristic diffusion distance. It was taken that the elimination of a spherical pore could be represented by the radial diffusion of vacancies in a cylinder of unit length, 3Dt and the equation r3 - r3 3 was derived, confirming k the proposal of Kuczynski, (in the discussion under Shaler, 1949) • 3 3 that the elimination of pores is given by r r K t. Evidence from Nabarro-Herring microcreep rates appeared to endorse this relation.

Navias (1956) attempted verification of the plastic flow theory of sintering by heating large (1000y..) single-crystal alumina spheres together in vacuo and hydrogen on a thin molybdenum saucer. There was some adhesion of the spheres, in the form of a bridge between the spheres, up to --,)0.12a in the best cases. One interesting result was that sapphire spheres sintered in hydrogen tended to lose their roundness, showing a tendency to form hexagonal facets, while the vacuum-sintered spheres remained unchanged. Contamination from the molybdenum appeared to be present in both cases. The technique of sintering large spheres was also used by O'Bryan and Parravano (1962), who studied rutile single - 26 -

crystal spheres. Slow initial sintering (time exponent n = 7) was followed by more rapid sintering (n = 2), and the appearance of facets was used to explain the change-over. The derived activation energy of 70 Kcal/mole and "scaling" exponent of 3 indicated volume diffusion. Similar experiments by Norris and Parravano (1963) on zinc oxide showed that no shrinkage occurred in the system, and rate-control appeared to be by an evaporation- condensation mechanism.

Burke (195ria)pointed out that, while it appeared that a limiting density had been reached for any one temperature in the sintering studies of Allison and Murray (1954) on sodium fluoride and calcium fluoride compacts, a treatment of the same data on logarithmic scales gave an approximately straight line for the linear shrinkage of sodium fluoride compacts, corresponding to the relation &/t2/5 Lo for up to about 8% shrinkage. However, similar treatment of the data for calcium fluoride gave an initial 0.4" slope which then decreased after a certain time at all temperatures. This decrease appears to be contrary to the theory, which would predict a decrease after a certain shrinkage rather than after a certain time. The copper sintering data of Clark et al. AV (1953) were likewise examined, and the relation - / 7V".0

1.2(i) ROLE OF GRAIN BOUNDARIES IN VACANCY ANNIHILATION.

Burke (1957a,b) also showed teat pores in alumina were preferentially eliminated near grain boundaries, as had been shown for copper by Alexander and Balluffi (1950). By examination of -27-

the published micrographs, it is not possible to determine whether grain boundary diffusion, where pores in the path of a moving boundary will be absorbed, was responsible for this effect, or whether it was caused by volume diffusion of vacancies to a nearby grain boundary sink, which will not only sweep out pores in the path of a moving grain boundary, but will also permit shrinkage of pores close to a stationary grain boundary. The micrographs clearly show sweeping out of pores by a moving grain boundary, but it is not possible to make unequivocal statements as to whether or not isolated pores shrink. In considering the role of grain boundaries in sintering, the term "vacancy sink" is sometimes used rather loosely to mean a place where vacancies are either annihilated or enter a faster-diffusing system whence they are transported to the annihilation site. It will be observed that the difference between these two situations is manifested in different shrinkage behaviour, and clear distinction must therefore be made.

Burke (1957b) pointed out that the findings of Balluffi and. Seigle (1955) for copper indicated the absorption of vacancies at grain boundaries by grain boundary collapse rather than the use of the boundaries as "pipes' to conduct vacancies to a surface at which they might be discharged. It was thought that observations on the effects of impurities on sintering indicated that volume diffusion to a grain boundary sink (in its strict seLse) was responsible for sintering.

Alexander and Balluffi (1957), who studied the sintering of copper wires on spools, considered that the observed shrinkage rates, temperature dependence of sintering, and scaling laws, all indicated a volume diffusion mechanism, and confirmed the preferential elimination of pores at grain boundaries, and adjacent to them. -28-

Harper and Dorn (1957) found that single crystal aluminium wires creep, but it was claimed that this did not invalidate the Nabarro-Herring mechanism, as it may be explained by the high stacking fault energy of aluminium. It does, however, indicate the degree of caution which must be taken in the interpretation of experimental observations in sintering and allied phenomena.

Quirk, Mosley and Duckworth (1957) found that smaller particles of beryllium oxide sintered faster than larger ones, but they were unable to derive a simple relation between particle size and sinterability. Stenquist, Mastel and Anicetti (1958) found the same qualititative relation for uranium oxide, and pointed out the wide range in surface characteristics - their agglomeration texture and shape - of different samples, while Livey et al. (1957) found that the particle size of magnesia, and hence its sinterability, not only varied with the temperature of calcination of the original magnesium hydroxide, but also very much depended on whether the calcination was conducted in air or in vacuo. Tresvyatskii (1958) found that the sinterability of magnesium oxide was enhanced by . vibratory milling.

1.2(j) DIFFUSION MECHANISMS AND SINTZRING.

Crank (1957) pointed out that caution must be exercised in the interpretation of diffusion phenomena, and the effect of the concentration gradients and distributions of one species on another must be investigated before such relations as Fick's equation can be used with confidence. It was also suggested that discrepancies between the results for diffusion coefficients obtained from conductivity methods and those from radioactive tracer methods might be attributable to an exchange or ring mechanism of diffusion, where two or more atoms change positions without vacancies being involved, and thus involving no net transport of matter. Though this mechanism 29 -

was thought to provide a negligible contribution to diffusion, the possibility had been pointed out, and it should be noted that such a mechanism would give rise to discrepancies between derived volume diffusion coefficients for sintering and those obtained by radiotracer methods.

Jost and Oel (1957) showed that the diffusion coefficient derived for sintering should correspond to that of the slower moving ion in a di-ionic system. Silver iodide sintering was shown not to be controlled by the diffusion of the faster-moving silver ion, thus indicating that the slower iodide ion is rate- Controlling, It was pointed out that ionic conductivity methods give the diffusion coefficient of the faster-moving ion.

Hiltmann and Spiess (1958) reported that they used the relation: d t = density at time t frF 2 d - d Kt = ( --Taz) , where x t - o s d = initial density d o p o d = powder density. to describe the sintering of titanium oxide, though presumably \ 1 - x was used in the equation. Activation energies of 51.5 Kcal/mole and 29.4 Kcal/mole for samples of different purities were derived. The formula is based on that of Jander (1927) for reacting powders. Other workers have used such "proportion gone" relationships, notably in the Japanese work summarised by Bockstiegel (1956).

1.2(k) DIFFUSION PATHS IN SINTERING.

Coble (1958) examined the question of diffusion paths and sinks for vacancies, and studied the sintering of aluminium and ferric oxides. The mechanisms considered were: - 30 -

(a) Vacancy diffusion from the neck surface to the grain boundary by (i) volume, (ii) surface and grain boundary routes, which would give both shrinkage and annulus formation.

(b) Volume diffusion of vacancies from dislocations in the interior of the grains to the grain boundary, giving shrinkage and neck growth, but no formation of an annulus.

(c) Vacancy diffusion from the neck surface to the particle surface by (i) volume, (ii) surface routes, giving rise to annulus formation only.

(d) Vacancy diffusion from the neck surface to dislocations in the grain interior, giving annulus formation only. . 4 32 )SS3D t For (a)(i) the neck growth relation (2\ 7 V was obtained, and the shrinkage relation derived for this modelk T was 3 2 (, D. t (L - Compared with the corresponding relations o kT (xv5_,_ 40483D t jaN5/2_ 20V(;3Dv t a/ -- 7 V , and! kT ‘Lo) a3 derived by Kingery and Berg (1955). While Kingery and Berg had tak,,n the diffusion flux as having cylindrical symmetry and diffusing away from the neck surface into an unspecified sink in the particle, Coble (1958) treated the flux as for heat flow to the surface of a surface-cooled, electrically heated cylindrical conductor, with the length of the cylinder taken as io (the equation used is that of a portion of an infinite cylinder), thus flux J = 41rDi\C. For (a) (ii) the relations derived were: , 3 6 96 D and I 3 a 4 D'3t a kT a kT - 31 -

These relations were modified in the case of rate-control by boundary re-creation to: 4 D and( 6/2-: X D >-'`C3t (a)a N 2 a kT LLB a2 kT assuming the same flux equation as before, but with the cylindrical length being taken as the grain boundary width

For the cases where diffusion of vacancies to and from dislocations occurs, the distances involved and the chemical potentials were uncertain, but the neck growth and shrinkage relations for model (b) were given as: *3 (L1,3/, tt • a' ' \ Lo / a3 5 t The relation (-x) a ae-i was accepted for volume diffusion of vacancies from the neck surface to the particle surface, model (c)(i).

In studying the neck growth rates during sintering of alumina, Coble took single crystal spheres (401-3000)A, and sintered them to smooth alumina plates for various temperatures and times, with various sphere sizes. The contact area was approximately circular, with a tendency to form hexagonal sides or scalloped edges, the latter of which had also been observed by Gwathmey and Dyer (1959) for copper. The asymmetry is due to the variation in surface energy with changing crystal and boundary relative orientations. The same phenomenon is probably responsible for the formation of terraces on sintered metal particles, observed by Christensen and Calbrick (1948). On plotting the neck radius against time on logarithmic scales, differentiation between time exponents of 1/5 , 1/6 and 1/7 was notpossible.

Shrinkage experiments were conducted with powder compacts of alumina (-0.20JA,) and haematite ( 0.13tA), both powders being composed of approximately spherical, monodisperse particles. The initial sintering models were expected to break down by 4-6% linear shrinkage. -32-

Logarithmic shrinkage vs. time plots gave slopes of 0.4-with some deviations, while the particle-size dependence approximated 1/a31 though the relation LL, 1 cannot be excluded, because of the L (1'‘ o a scatter. Thus the question of whether volume diffusion to the grain boundary or grain boundary diffusion is rate controlling had still not been satisfactorily answered. It was also pointed out that when both surface and grain boundary sinks are operative, the apparent diffusion coefficient, D*, will be a composite of the surface and boundary coefficients (Ds & Db respectively), and the relation D* = 2/3Db + 1/3D was proposed. Further, the question s of a reduction in the shrinkage rate in such a case must be considered, as only a grain-boundary sink can contribute to shrinkage.

Diffusion coefficients were calculated for alumina on the basis of YDlume diffusion to the grain boundary, using both the Kingery and Berg (1955) and Coble (1958) models, with suitable adjustments to fit the case of sphere-plate sintering. The data of Coble (1958) fitted straight lines for both the models, with an activation energy for sintering of 165 Kcal/mole for the Kingery and Berg model, and 180 Kcal/mole for the Coble model, which is comparable with the activation energy of 152 Kcal/mole determined by Oishi and Kingery (1960) for oxygen ion diffusion in alumina single crystals. The sintering of haematite appeared to confirm previous indications that F 3+ e diffusion was rate-controlling. Coble (1959) pointed out that in the model (d) of Coble (1958) vacancy diffusion from the neck surface to dislocations inside the particles could give rise to shrinkage by withdrawal of an edge dislocation insert plane and subsequent collapse. Assuming a random orientation of dislocations, an effective uniform decrease in particle radius would occur. This mechanism was rejected, however, because it does not require the existence of grain boundaries which had been observed to be a prerequisite of sintering. - 33 -

Quirk (1959) found, in a dilatometric study, that the sintering of dead-burned magnesium and beryllium oxide powders showed agreement with Kingery and Berg's tL (,< t0.4 relation for L

volume diffusion of vacancies to grain boundary sinks, but active powders gave a high initial rate of shrinkage, followed by a lower subsequent rate, where AL ,, 0.1 .A. t L0 Kuczynski, Abernethy and Allan (1959) sintered alumina spheres to spheres and plates in dry hydrogen, helium, wet hydrogen and oxygen atmospheres in various types of furnace. The neck diameters were measured, and for wet hydrogen, helium and oxygen the(x)5 t relation was found to hold approximately, any variations tending to produce exponents of less than 5. While the contact areas formed in helium and oxygen were smooth and usually circular, the necks formed in wet hydrogen showed hexagonal tendencies or scalloping.

In dry hydrogen, Kuczynski et al. found that neck growth occurred which could be represented by two straight lines on a logarithmic plot ofA vs. t, the two lines being separated by an upwards kink, situated at (!)00.12 - 0.20, increasing with xe5 temperature. For the shorter times the relation was ,t, (where x*, derived, and for longer times the relation (a1C.*) 3, t* are the values (x-x ), (t-t ) for neck growth and time on the o o upper part of the curve) was found to hold. The spheres themselves take on the appearance of peeled oranges, with hexagonally symmetri.- cal longitudinal grooves, and at higher temperatures (1900°C.) form faceted crystals, as was observed by Navias (1956). It was concluded that volume diffusion was responsible for alumina sintering in all atmospheres, and activation energies of 135 Kcal/mole for wet hydrogen, helium and oxygen atmospheres, and 230 Kcal/mole for a dry hydrogen atmosphere, were reported. While the former value -34-

is comparable with the value of 165 Kcal/mole reported by Coble (1958), with an apparent absolute diffusion coefficient about ten times that of Coble (1956) in the same temperature range, the latter value is unexplained.

The later stages in the sintering of alumina were explained by the evaporation-condensation mechanism (by Kuczynski et al.), supported by the observed high rate of evaporation of alumina. It was suggested that the alumina was reduced by the hydrogen to lower oxides of aluminium, which were more volatile. However, because of the rapid flow of gases through the furnace, the equilibrium required for sintering to occur in a way described by the derived models was probably not obtained, and it was also observed that the neck area did not become as rounded as was expected. The temperature dependence gave an activation energy of 225 Kcal/mole, the same as for the initial stage of sintering in the same atmosphere, when the diffusiOn mechansim was postulated. It was considered that the phenomenon could be explained by the theory of Herring (1951) for the effect of a grain boundary on neck growth by diffusion at the intersection of two crystals: x3 cos 0 ( acute angle between neck surface and extension of grain boundary), but the effect of the grain boundary on the geometry of the neck, and subsequent modification of the neck growth relation, should not be ignored. Several questions are still outstanding. Foremost among these are (i) why is the apparent diffusion coefficient so high, and (ii) why is there a sudden kink in the log —a vs. log t curve instead of a gradual change- over from one time-dependence to the other?

It was claimed that diffusion of interstitial aluminium ions might be rate-controlling for non-reducing atmospheres, and that the large number of oxygen vacancies introduced during dry hydrogen sintering might make the diffusion of oxygen ions rate-controlling in that atmosphere. This would give activation energies of the order of -35-

140 Kcal/Mole and 230 Kcal/mole respectively. Apart from the fact that the slower-moving ions (i.e. those with the lower value of the absolute diffusion coefficient) should be rate-controlling, it appears from the work of Coble (1958) that oxygen ions are rate- controlling with an activation energy about 165 Kcal/mole, and it thus seems unlikely that this hypothesis can be substantiated. However, if transport is by surface diffusion, an increase in the number of oxygen atoms desorbed with increasing pressures of hydrogen might lead to a change-over from aluminium ion to oxygen ion rate-control (if aluminium ions are initially rate-controlling).

A plot of the reciprocal of the induction period for the appearance of facets during sintering against reciprocal temperature yielded a straight line corresponding to an activation energy of 140-150 Kcal/mole. The process of formation appeared to be nucleation and growth from the neck area. What appeared to be visdous 2 flow sintering (x in wet hydrogen in a tungsten-heated furnace was explained as being due to the formation of a glass by tungsten oxides reacting with the alumina. It is interesting to note that the single-crystal cadmium sulphide prepared by Fass and White (1966), by heating a powder compact for several hundred hours, had similar faceting.

The work of Kuczynski et al. (1960) provided further impressive evidence for sintering occurring by a diffusion mechanism. Copper- Indium alloy wires (oat. - % In), which are just within the solubility limit at 485°C., were sintered together on a mandrel The indium diffuses faster than copper in this alloy and thus a more and more concentrated solution would be expected at the deposition point if material transport by diffusion occurs. Sintering at 6900C. followed o by "ageing" at 485 C. led to the precipitation of indium-rich p,-phase., proving diffusion had taken - 36 -

Kingery (1960) noted the lack of shrinkage during the sintering of ice, and also found the neck growth relation to be (—x) 7 t , in agreement with Kuczynski (1949a) and Herring a (1950a) for the surface diffusion mechanism. However, the findings of Cabrera (1950) and SChwed (1951) should not be overlooked.

Hornstra (1961) considered that it was possible for grain boundary sliding to contribute to densification by elongation of a spherical pore. It should be noted that such a mechanism re- quires spherical pores on grain boundaries, and that those boundaries be sigmoidal in shape. In all the published photomicrographs such an unstable boundary shape has not be observed, and pores on grain boundaries tend to be elongated anyway, though pores at grain boundary intersections (grain edges and corners) are more rounded. This mechanism may take place to relieve stresses during grain growth, but it is difficult to visualize how this can contribute a great deal to sintering, except, perhaps, in the process of "hot-pressing". The mechanisms of transport in this process are beyond the scope of this thesis, and the reader is referred to the papers of McClelland (1961), Coble and Ellis (1963), Kingery, Woulbroun and Charvat (1963), Vasilos and Spriggs (1963), and Rossi and Fulrath (1965) for consideration of hot-pressing mechanisms.

1.2(1) THE INTERMEDIATE STAGE SINTERING MODEL:

Coble (1961) considered the kinetics of sintering after the initial sintering had taken place, and the necks had grown to such a size that the theory for initial sintering broke down. The further sintering could be considered in two stages, (i) the inter mediate stage, involvihg open-pore sintering, and (ii) the final stage, where the isolated pores shrink. For both the stages, volume - 37 -

diffusion of vacancies to a grain-boundary sink was considered to be the densification mechanism. Coble considered that grain growth occurred at the end of the initial stage of sintering, when the neck area was wide enough in comparison with the grain area for the grain- boundary to move from the neck.

It was assumed that sintering and pore shape change had occurred to such an extent that the system could be satisfactorily represented by perfectly fitting tetrakaidecahedra (formed by cutting an octahedron at its six apices, with the cuts on the edges being at 1/3 of the original edge length from the apex), fitted with continuous cylindrical pores all along the 36 equally-long edges. The axis of a pore is taken as coincident with an edge, which is shared by three tetrakaidecahedra. In the final stage of sintering, it was considered that the remaining pores were coincident with the 24 corners, each of which is shared by four tetrakaidecahedra.

For the intermediate-stage case, diffusion of vacancies was considered to occur from the pores to the square and hexagonal faces (grain boundaries) which they surround. The faces were then considered circular, and it was assumed that the grain boundary absorbed an equal flux for all its area. By regarding the diffusion flux as analagous to heat flux in a surface-cooled electrically heated conductor (segment of an infinite cylinder), with the length equal to the pore diameter, and allowing for an increase in flux by a factor of two because of its divergence, the relation derived was: P = porosity 10 D 3 (tf - t) 1 . edge length P f 13 k T = time for shrinkage of pore to zero radius. For grain boundary diffusion the relation derived was: w y 3 0 2/3 P 1 " w = boundary width. 1 k T -38—

For the final stage of sintering, where the pores are considered to be spherical and at the 24 four-grain corners, it was assumed that the flux could be represented by diffusion between concentric spherical shells. There are two cases to be considered, for which the radius of the pore (i) is, and (ii) is not, negligible compared with the characteristic diffusion distance.

(i) When the pores are small (P = 0 - 0.02):

6-riDW(tf t) P - 3 42 1 k T (ii) When the pores are comparable in size with the diffusion distance d: 4 r3 r 3):,,3t 3 - Trd k T

The case of shrinkage of pores when they are not at the four-grain corners, but only at or near a grain boundary, was less easy to analyse, though it was expected that the shrinkage should still obey the relation rkt approximately.

It was pointed out that the grain growth relation for alumina had been observed as G3 - G 3 = At, where G, G are o o the observed and initial grain sizes respectively, and A = const.. As G.<1, Go<::G, and, for intermediate and final stage sintering dP Tcc E3 dt = 3 , then dP At kT , which was integrated to: 1 kT

-1 o 1 -ND 3 t -I' o A k T • -!t o where P o porosity at end of initial stage sintering. Variation in the constant N due to the slightly different cases involved in intermediate and final'atage sintering will cause curvature in a P vs. In t plot. - 39 -

In the sintering of alumina compacts, the derived diffusion coefficients were very much higher (by a factor of -105) than the oxygen ion diffusion coefficients for volume diffusion in alumina single crystals reported by Oishi and Kingery (1960), though oxygen ion diffusion in polycrystalline alumina was faster, but with a lower activation energy (152 and 110 Kcal/mole respectively). The activation energy for intermediate-stage sintering was given as 150 Kcal/mole, comparable with the activation energy for grain growth (153 Kcal/mole). Previously determined values for the sintering temperature dependence, 145 and 165 Kcal/Mole, were also comparable. This equivalence of temperature dependence for sintering and grain growth was thought to be due to a dependence of grain growth on the removal of pores, as the activation energy for grain growth would normally be expected to be that of grain- boundary diffusion, which is less than that of volume diffusion.

Similar semilogarithmic relationships have been obtained by Coble and Burke (1963) by re-plotting the sintering data of Belle and Lustman (1957) for uranium oxide, and Walker (1955) for alumina.

1.2(m) FURTHER WORK ON THE SINTERING OF OXIDES.

Whitmore and Kawai (1962) found that initial sintering of titanium oxide obeyed the volume diffusion equations given by Kuczynski (1949a) and an activation energy of 74 Kcal/mole was derived.

Bruch (1962) studied the sintering of alumina in a hydrogen atmosphere, and found that "normal" sintering could be fitted to the relation Pax t0.4, while "subnormal" sintering, which occurred at lower green densities and lower temperatures, showed a time dependence to a power of less than 0.4. _ 40 _

For "normal" sintering, the equation log10 P A - 0.434 fri94i, nlogiof, i-z 0.4, log10 A = function of green density = 10 log10 Po - 23.43, gave an activation energy Q = 150 Kcal/Mole, while for "subnormal" sintering, an activation energy of 275 Kcal/mole was obtained. The Cause of "subnormal" sintering was not known, but it was suggested that it might be some pore clustering effect which was temperature-dependent. It is interesting that a replot of Coblels data (1961) on a log P vs. log t scale gave slopes of 0.4 for all but the longest times. Livey and Hey (1964) found that their data on beryllium oxide sintering fitted the Bruch analysis, with activation energies of 100-140 Kcal/mole, depending on the nature and quantities of impurities.

McQueen and Kuczynski (1962) drew attention to the possibility of different mechanisms being predominant at different temperatures, as neck growth measurements for vacuum sintering of polycrystalline zinc sulphide appeared to indicate surface diffusion (activation energy 5.7 Kcal/mole) below 600°C., and volume diffusion (Q = 26.4 Kcal/mole) at higher temperatures. Both the activation energy and frequency factor in surface diffusion were strongly atmosphere- dependent. A similar observation was made by Kostic and Ristic (1964), who found that the models of Pines (1946) and Kingery and Berg (1955) did not fit their data for the sintering of uranium oxide, and considered that the sintering process, which appeared to occur in two stages (at 800-1100°C. and 1100-1300°C.), fitted the 8V n relation —Vo = kt , where both k and n were temperature dependent. Iwasaki (1965) considered that a mechanism change-over occurred in the sintering of Pb(Ti, Zr)03 solid solutions, a bulk diffusion mechanism explaining the sintering when less than 20 mole% of.Zr0 2 was present,. surface diffusion occurred at >20 mole % Zr02; the derived activation energy decreased with increasing zirconium content. - 41 -

1.2(n) REVISION OF THE INITIAL-STAGE SINTEING MODEL,

Johnson and Cutler (1963) examined initial-stage sintering by graphical methods, considering both volume and grain-boundary diffusion mechanisms for various contact geometries. The geometries chosen were spherical, parabolic, and cone-on-plane, and also spheres with the neck between them grooved because of the grain boundary. For various amounts of overlap of the two surfaces, the neck radius, radius of curvature of the annulus, and area for diffusion (in the case of volume diffusion) were measured, and the volumes of the annulus and the overlap were equated. Cylindrically symmetrical diffusion inwards from the neck to the grain boundary, or inside the grain boundary, was assumed to occur. The shrinkage equation given was:

61, ( Kvc3 D ',mtm K = const. vary const. with Lo \kT aP m = const.: geometry

For volume diffusion the time dependence, mi was found to be 0.46 (except for the 160° cone-on-plate model : m = 0.33), and the particle size dependence, p, was 3 (except for the paraboloid: p = 2). Grain boundary diffusion showed a time-dependence m = 0.31 (except for the cone-on-plate: m = 0.25) and particle size dependence p = 4, (except for the paraboloid: A, = 3). For bulk diffusion with spherical particles it will be seen that Kingery and Berg (1955) and Coble (1958) had found m = 0.40 and m = 0.50, respectively, and p = 3, and Coble (1958) had found m = 0.33 and p = 4 for grain boundary diffusion, with m = 0.5 and p = 2 for boundary re-creation rate-control. It is very doubtful whether the shrinkage equations can be applied for L as high as 0.06. The neck growth relation was given as: 0 (x)n F.''',5 (3 K' constants Dt depending a k T aS on geometry. - 42 -

For two spheres n = 4.7, s = 3 for volume diffusion, and n = 7 , s = 4 for grain boundary diffusion.

For comparable contributions of grain-boundary and volume diffusion, the relation derived was:

K" Ta3/ i., ( 6L 42.2 11 V 17 / A I o , d ( -17 ) = dt 0; ail + 16-1 b 1 Db ) tLo' ----100a t.1 7v- ,

4L 16 rr. b ( Db\ If I: volume diffusion would be operative, and if 0 100a Dv)

6L 16-rr b (DO then grain-boundary diffusion would be rate- L looa Dvi v controlling. As D—v increases with increasing temperature, I volume diffusion was expected to be favoured for higher temperatures as well as for larger particles, and grain-boundary diffusion was expected to be of increasing importance at lower temperatures pnd for smaller particles. Thus high temperature experiments with material of which the geometry is observable might well display a different sintering mechanism from that which is occurring in powder compactb.

It was assumed that the irregularities of the compact and the unknown, effective time of the start of - Sintering owing to the effect of the heat-up period, would give rise to a small shrinkage error and a small time error,but the compacts would otherwise behave ideally. The time error, St, was determined as that correction applied to the times for a given isotherm which would straighten the m L vs. t curves, and the shrinkage error, NL, as the difference between L 0 and the extrapolated length at t =0 for that isotherm. - 43 -

Shrinkage studies for alumina compacts gave a value of almost independent of temperature, and thus a good indication of the time exponent, m, was given by logarithmic shrinkage-time curves for sintering at higher temperatures. There may possibly be a change-over of mechanism on the basis of this model, as there is a tendency towards grain-boundary diffusion being faster at lower shrinkages, and volume diffusion at higher shrinkages. It may be noted that if there is a change-over, then unless the change is clear from the logarithmic shrinkage-time curves, an intermed iate value would be obtained, and the curve-straightening procedure would give meaningless results.

Johnson and Cutler conducted a dilatometric study of the shrinkage of compacts of various alumina powders (0.2-20y.), and by use of a shrinkage correction SL up to 2% Lo, with cCli of the same order for any one powder at all temperatures, and a time o correction of not more than 4 mins. for temperatures above 1400 C. but up to 50 mins, for lower temperatures plots of L vs. 10.31 gave straight lines, and thus a grain-boundary diffusion mechanism was deduced. A derived activation energy of 142 Kcal/mole was obtained for one alumina powder, and 150 Kcal/mole for the others.

The time dependence, indicating a grain-boundary diffusion mechanism, was also found by Anderson (1965), who found that the initial sintering of barium titanate gave a time exponent n = 0.31 ± 0.03. It is interesting to note the results of Aitken (1960). One batch of beryllium oxide gave n = o.40, while others gave n = 0.33 for the initial stage of sintering. For one calcine, the slope started at ,0.5 and decreased to

1.2(o) FURTHER WORK ON THE INTERMEDIATE STAGE OF SINTERING.

Morgan (1963) studied the shrinkage dilatometrically of a wide range of single and mixed oxides. The shrinkage was measured

-44-

4L corresponding to the initial stage and usually for Lo— the first part of the intermediate stage of sintering, and it was t held well for shrinkages in the found that the relation LLL o initial stage, and could be applied with varying success for higher shrinkages. Deviations from the initial straight line were towards faster sintering with some oxides (magnesium oxide, stannic oxide, ceric oxide) and slower sintering with others (ferric oxide, nickel oxide, titanium dioxide, niobium pentoxide); a different effect was obsafWed at different temperatures for cadmium oxide, zirconium dioxide, etc. This does not necessarily mean that the semilogarithmic relationship is being disobeyed by more than a change in the value of LI, 1 a the proportionality constant. As —-V for small shrinkages, L o the relation was expressed as: o D = density at time t D D k in t o D initial density. which is equivalent to Coble (1961)'s relation P _ -NDW1nt A k T The temperature dependencies represented by activation energies were found to be in the range 11-14 Kcal/Mole for magneisium oxide, stannic oxide, ferric oxide, and cadmium oxide,(and in the range 24-28 Kcal/mole for aluminium oxide, ceric oxide, nickel oxide, titanium dioxide and Zr Ca Zirconium dioxide sub- 0.95 0.05_01.95 stituted with 10-30 mole-% calcium oxide gave activation energies in the range 35-41 Kcal/mole, while zirconium dioxide (67.4 Kcal/ mole) niobium pentoxide (107.9 Kcal/Mole) had higher values for the activation energy.

It was pointed out that the temperature dependencies of both diffusion and grain growth would contribute to the "activation energy" of sintering as?' -t d/cAT D '6" .) = t.! (Or. e 6 A i< Tr ter (A,,,e/P3-) The slope in a density or porosity vs. log t plot will give the logarithm of this expression as it8 slope i.e. : (Ed - ) lo (const.) - T - '10 '10 2.303 P.T -45-

Thus the "activation energy" for sintering should be given by (E E ), as log T is approximately constant. d gg

Brown (1963) also found that the relation P a log t could be applied to sintering data, and found obedience for the intermediate stages of sintering (of calcium oxide, magnesium oxide and nickel oxide) for temperatures up to 1500°C. Sintering data for magnesium oxide doped with 0.01 cation-% vanadium were found to fit the relation Egoct. (A = density) Chaklader and Thiriar (1964) attempted to fit the Coble (1961) model to sintering data for titanium dioxide, but were unable to find any correlation between the activation energy for sintering and those of oxygen ion diffusion and grain growth. (Grain growth 2 fitted the relation G - Got = kt, which is contrary to the requirement of the Coble model that G3 cc t). Table 1.2. shows the relation between the temperature dependence of sintering (obtained from semi-logarithmic plots) and activ- action energies for grain growth and for the volume diffusion of the anion and cation. -46-

Table 1.2 Activation Ener0.es (Ln Koal/mole) for diffusiaa,grain growth, and sintering. Small superscripts : references.

(Cation) E Notes OXIDE Ed (Anion) Ed gig. E sinterinq

**110 1 3 1%4 a.Polycryst. & AI 0 1141' 5.5 2 3 152a, 1534* 24.655 single crys. resp. • __ . Ca0 81' *1101 44.3''

Ca Zr,_,••,,, 0,•1 Both82.99 Zr 61.8" 29.8° ,.is 4,.;,s 9 -,1. Ca 98.8" 35.4,5 C ,,..Zrt,,s,q94 Both109q 80-91'2

Cd0 93's 99!t. 11.85 4 4 Cr 0 ** , 100 2 3 101' 88,7n 610.1 • hi Fe203 146 11224' 14.0' u Mg0 62.4° 79.0 +60' 12486 b.Doped with 0.1 62 b. 2740' cation % V. Nb2 05 52-3 2+ lO7R94' -- ..._ 56l' 18.4' 9 c.Calcined at 44.227' 26.5!' higher temperature Ni0 54" **-4'2'3 +551 24'31' d.Calcined in 45.621 22."9d oxygen. 48 3°

12616 14.2s SnO2 118.7v 14.55 .5 74ez 26.4 e. Calculated from TiO **7414e. +130;4 118 3µ initial sintering 2 6011 data.

3? U0.7 29.7'f. 8e 87 f.Non-stoichiomet- ric, g. ctoichiom. 65.3./4g. _ e ZnO 16511 [ 73.7 "` ' 97.7 - 734' 1 L 43.5'' , ** Claimed to be the2slower2 or slowest diffusing ion. 4- Calculated from G - Go = kt plots. -47-

'Oishi & Kingery (1960a) 2211ndner & Parfitt (1957) tPaladino & Kingery (1962) LINicholson (1963) 3Cutler & Newbold (1958) & Lyubimov (1963) 4Coble (1961) 260'Keefe & Moore (1961) 'Morgan (1963) 6Lindner, Austrbmdal & Akerstrom (1952) 'Daniels et al. (1962) 26Lindner and 1-cerstrom (1957) ''Brown (1963) ImShin and Moore (1957) 9Rhodes & Carter (1962) "lid-1 (1958) Kingery et al. (1958) 24Choy and Moore (1962) "Mobius, Witzmann & Gerlach (1964 Mlotsman et al (1962) & Subbarao (1963) & Enqvist (1956) Maul, Just & Dilmbgen (1961) mWhitmore & Kawai (1962) 'Haul & Just (1962) & Dambgen (1965) 'Hagel (1965) 34Chaklader & Thiriar (1964) "'Lindner (1955) 3-5Auskern & Belle (1958) "Fedorchenko & Ermolovich (1960) '9'Auskern & Belle (1961a) 'Hagel & Seybolt (1961) 'Auskern & Belle (1961b) `Kingery, Hill & Nelson (1960) m MacEwan (1962) ``Lindner (1952) Moore & Williams (1959) (1952) 'Oishi & Kingery (1960b) "Lindner, Campbell & Akerstrom/ 44Secco & Moore (1955) It may be seen that for magnesium oxide, the activation energy for sintering (12.8 Kcal/mole) found by Morgan (1963) lies between the values of 0.4-2.4 and 17-19 Kcal/mole for (Ed - Egg), and that reported by Brown (1963) is well above the differences. The hypothesis of Coble (1961) that the grain growth activation energy was dependent upon that of diffusion, ignoring the effect of the two temperature dependencies in the densification equation, was not confirmed by Chaklader and Thiriar for the sintering of titanium oxide. For those oxides for which information is available on all four activation energies (aluminium oxide, zirconium dioxide doped with 15-16 % calcium oxide, magnesium oxide and nickel oxide), the relation reported by Morgan (1963) does not apply, and Coble's hypothesis can be seen to apply only for alumina, and possibly for magnesium oxide.

The large difference between the activation energies for sintering found for oxides prepared by Morgan (1963) and Brown (1963) and those of Coble (1961) and Chaklader and Thiriar (1964) further -48-

indicate the caution which must be exercised in the interpretation of sintering data.

Clare (1966) also observed that the relation E s = Ed - Egg should hold for the intermediate and final stages of sintering. In a study of the kinetics of sintering of beryllium oxide compacts, the Coble (1961) relation P = K - K 1n t was found to apply for 1 1050-1400°C, and for shorter times at 1500°C., but for longer times at 1500°C. the relation given by Bruch (1962) was obeyed. Not only is there considerable scatter in the data, but in the P vs. log t plot the straight lines were arbitrarily drawn from log t = 0 (t = 1 min.), which does not give the best straight lines. Grain growth appeared to obey the law G3 3 - Go = At required by the Coble model, though there was considerable scatter, and a much higher rate for longer times at 1500°C. The initial-stage sintering of beryllium oxide, up to 3% linear shrinkage, was found to obey the relation LLcct- and the slope then fell off to -,1/5. Derived diffusion coefficients from the initial-stage model gave an activation energy of 138 Kcal/Mole, and the absolute values were one to two orders of magnitude lower than those from the intermediate stage sintering model, which may also be observed from the data of Coble (1961) for alumina.

The activation energy for sintering was 31 Kcal/mole, and that of grain growth -104 Kcal/mole. While E = E ^,135 d gg Es Kcal/mole was of the same order as the activation energy for "diffusion" in the initial stage, this does not correlate with the measured activation energy for diffusion of the oxygen ion (the slowest ion), and the absolute value of the derived diffusion coefficient is well above the measured oxygen ion diffusion coefficients for most of the temperatures used. -49—

Table 1.2. (continuation) below gives similar data for BeD. Table 1.2. (contd.) Activation energies (in Kcal/mole) for diffusion grain growth, later sintering and initial stage sintering.

E (0) E (Be") E ES(interned) E (initial) d d gg s

66.1' a 434 62.544 47 41 Be0 36" a 111.6`° b 104 31 138 47 64%92"b 92 4E 111+"

4!tusterman, Meyer & Sviarthout (1961) 'Austerman (1964) a Polycrystalline, ) 173000. b. Polycryst. < 1730°C. "DeBruin & Watson (1964) 45Austerman (1961) 'Chang (1958) 47Clare (1966)

1.2. (p) Recent Work on Diffusion and Sintering in Oxides.

Bolling (1965) drew attention to the competition between coalescence and shrinkage of pores, and its possible effect on sintering kinetics.

Bagel, Jorgensen and Tomalin (1966) studied the initial sintering of chromium oxide, chosen because the diffusion coefficients for volume diffusion of cation and anion differ by a factor of 3 4 10 -10 , a much greater difference than for alumina or ferric oxide. The data were compared with the relations of Coble (1958)

(i.e. t0.5 for volume diffusion, and t0.33 for L LL LLo o AL 0 grain boundary diffusion), Kingery and Berg (1955) ( Lo t •4 for volume diffusion), and Johnson and Cutler (1963) i.e. AL 0.46 AL 0.31 7 ac t for volume diffusion and E-m t for grain -50-

boundary diffusion). The volume diffusion models were fitted fairly well, while the grain boundary diffusion models were rejected. Derived diffusion coefficients were within an order of magnitude of the oxygen ion volume diffusion coefficient for chromium oxide reported by Hagel (1965). The activation energies for sintering derived from the relations of Coble, Kingery and. Berg, and Johnson and Cutler were 101.6,123.0 and 109.9 (all within + 8) Kcal/mole respectively, compared with the activation energy 100.8 + 1.6 Kcal/mole for oxygen ion volume diffusion (Hagel, 1965).

There is thus still some question whether sintering occurs by grain boundary diffusion or volume diffusion to a grain boundary sink.

The claim of Paladino and Coble (1963) that, in alumina, sintering rate-control was by volume diffusion of aluminium ions, because the normally slower oxygen ions move by faster grain boundary diffusion, was questioned by Hagel et al. It was argued by Paladino and Coble that anion diffusion in polycrystalline alkali halides was greater for smaller grain sizes, and the ratio of the diffusion coefficient in single crystals tc that in polycrystalline specimens was proportional to the grain boundary area (see Barr et al., (1960). If this were also true for oxides, then the higher absolute diffusion coefficients in intermediate stage sintering could be explained by the mechanism.

Coble and Gupta (1965) indicated that Coble's application (1961) of the intermediate stage sintering model to the experimental data was in error, though the nature of the error has yet to be revealed.

Wuensch and Vasilos (1964) studied the diffusion of 2+ Ni ions into magnesium oxide by heating vapour deposition and "sandwich" couples. The concentration distributions, determined by electron microbeam probe spectroscopy and X-ray - 51 -

absorption analysis, appeared to indicate that grain boundary diffusion was the main transport mechanism in magnesium oxide below 1700°C., whereas volume diffusion predominated above that temperature. It was claimed, however, that the effective "grain boundary" stretched over distances of microns rather than a few atomic diameters. Wuensch and Vasilos (1962) found 2+ that the activation energy for such diffusion was: Fe 1.81 2+ 2+ ev., Co 2.06 ev., Ni 2.10 ev. It was claimed that there was a correlation between the activation energy for diffusion of transition metal ions into magnesium oxide and the ratio of the ionic radius to the electron polarisability, and between the frequency factor and the cube of the cation radius, suggesting that the same mechanism occurred for all the transition metal ions studied. However, the values given for the activation energies of transition metal ion diffusion in magnesium oxide 2+ 2+ by Zaplatynski (1962) are so different (Co 2.83 ev, Ni 1.57 ev.), that it is not yet possible to draw firm conclusions from such results. Shelley, Rigby and Cutler (1962) claim that in fairly 2+ pure magnesium oxide Co and Fe 2+diffuse by volume diffusion with a penetration frontier which is not advanced at grain boundaries, while in less pure magnesia it is possible that grain boundary diffusion was occurring. It was suggested that some of the transition metal was oxidised to Fe3+ or Co3+, creat- ing so many vacancies that the bulk was as efficient a diffusing medium as was a grain boundary.

1.3. THE F7EIOT OF ADWTIVES Af:D ATL,;SITHER,CS 01\1 SI4T4RING. (a) Introduction.

There are several possible mechanisms by which additives and atmospheres can affect sintering. (a) If the additive forms a. eutectic with the solvent crystal, the resulting liquid phase will have an effect on -52-

sintering, the magnitude of which depends on the quantity of eutectic, relative surface energy, solubility of the solvent in the eutectic, and other associated properties. For further consideration of such liquid phase sintering phenomena the reviews previously mentioned and the papers of Kingery et al.(1961) and Kingery et al.(1963) may be consulted.

(b)If the additive forms a second phase, inhibition of grain boundary migration, pinning of dislocations, etc., may affect the sintering kinetics.

(c)Surface effects either at the pores or grain boundaries, caused by the additive may alter the sintering kinetics. An example of this is the possibility that additives with polarizable cations (e.g. transition metal ions) may counteract the repulsive effect of the preferential oxygen outer layers on oxide particles, and thus enhance diffusion.

(d)Atmosphere or additives may cause a substantial vapour pressure of a compound of the solvent crystal, giving rise to vapour phase transport which will modify sintering kinetics.

(e)Altervalent ions may increase or decrease the number of vacancies available for diffusion, or may affect the diffusion rate of the species of opposite sign. Stressing the lattice may be another way in which altervalent ions affect sintering kinetics.

The difficulty of sintering pure magnesium oxide was recognised as early as 1918 by Ferguson. Malquori and Cirilli (1939) published data on sintering magnesium oxide with various additions, from which it appears that ferric oxide (5-10%) promoted sintering considerably, especially in the presence of calcium oxide (2-5%), while silica inhibited sintering or reduced the effect of other additives, and alumina appears to have promoted sintering somewhat, though increasing quantities reduced the shrinkage. Alumina -53-

(2.5%) with some calcium oxide (1.4%) gave a 5% dense body after 4 hours at 1550°C., though this combination was still not as advantageous as the Fe203 - Ca0 combination. Tanaka (1939) noted the greatly enhanced sintering of magnesia doped with iron oxide, and some enhancement with titanium oxide, and Letort and Halm (1947) found that grain growth in magnesium oxide was increased by additions of ferric oxide and silica, while Colegrave, Richardson and Rigby (1949) noted that purer magnesite rocks were more difficult to dead-burn than less pure rocks.

Johnson and Curtis (1954) pointed out that the as-prepared impurities in magnesium oxide affect sintering, and ascribed enhancement to liquid-phase formation.

1.3. (b) The Importance of Solid Solutions.

Marshall, Enright and Weyl (1954) showed that an addition of tervalent ions (A13+, Ga3+ ,Fe3+ , etc.) usually retarded the sintering rate for zinc oxide, while lithium oxide caused shrinkage at lower than usual temperatures. It was claimed that the lithium ions effectively increased the concentration of interstitial zinc, while the tervalent ions decreased the concentration of interstitial zinc and hence the matter transport rate. However, the work of Lee and Parravano (1959) and Moore and Williams (1959) leaves some doubt whether interstitial zinc diffusion is rate-controlling. The assumption that the cation diffusion coefficient is the main consideration in sintering has led to explanations of nearly all additive effects on a vacancy creation basis, despite indications that oxygen ions are the slowest moving, in magnesia and alumina at least. Thus for magnesium oxide the magnesium ions were reported by Lindner and Parfitt (1957) to have a -54-

,0 diffusion coefficient D = 0.249 exp (-79 00) while the diffusion RT ' 6 coefficient for oxygen ions was given as D = 2.5.10 -62 4oo exp ( .RT1.- ) by Oishi and Kingery (1960b).

1.3. (c) Surface Effects and Solid Solutions. Pampuch (1958a,b), advocating a viscous flow mechanism for sintering, considered the surface energy to be the most important factor. Additives would decrease the surface energy and hence decrease the "sintering temperatures". It was considered (Pampuoh3 1959) that 1-2% of additives, forming solid solutions, would have the optimum effect. Atlas (1957) found that lithium compounds aided the densification of magnesia, and the polarisable chloride and bromide had most effect, shown also in better compaction. The enhancement was explained on the basis of the surface activation theory of Tacvorian (1954)4 where local solid solution at grain boundaries and surfaces aids densification,the solute being slowly absorbed into the bulk of the material, or eliminated by evaporation. However, sodium fluoride had no effect.

Calderwood and Wilder (1957) noted that up to 12 mole-% of calcium fluoride promotes densification of magnesia. Jones, Maitra and Cutler (1958) made quite large (8 mole%) additions of zirconium dioxide, titanium dioxide, and ferric oxide to magnesia, and of titanium dioxide, manganese carbonate, chro!:lic oxide and ferric oxide to alumina, and sintered in oxygen, nitrogen and hydrogen. All three additives enhanced sintering in magnesia, though titanium dioxide was somewhat less effective in neutral and reducing atmospheres where some reduction to Ti3+ took place, and iron oxide was ineffective in hydrogen cs reduction to iron took place. The additions to alumina were less effective, and only manganous oxide (from manganese carbonate) and chromic oxide in nitrogen and hydrogen aided densification. -55-

Nelson and Cutler (1958) found that lithium oxide was the only oxide of the alkali metals and alkaline earths which did not inhibit magnesia sintering, and concluded that the lithium oxide must enter into solid solution and enhance sintering by anion vacancy creation. Silica and alumina inhibited sintering, except for silica at 1400°C., when a solid solution with excess cations was claimed to aid sintering. Titanium dioxide and zirconium dioxide both aided sintering, and the rounded grains in.the polished sections of titania-doped magnesia indicated the presence of a liquid phase. Chromic oxide inhibited sintering greatly, while ferric oxide enhanced, and this was explained by the theory of Weyl (1952) that sintering should be enhanced by the formation of cation vacancies. It was considered that the effectiveness of an additive was due to the extent of solid solution and the number of vacancies created. Curtis and Johnson (1957), who doped thoria with calcium oxide and calcium fluoride, also claimed that vacancy creation in substitutional solid solution caused enhancement of sintering. + Layden and McQuarrie (1959) found that Li and Al3+ aided sintering of magnesia for additions up to 1%, and Fe3+ aided up to 3%, while Cr3+ greatly inhibited sintering except for concentrations below 0.1%, when it enhanced sintering. Silica, titanium dioxide and zirconium dioxide also aided sintering, while Na+ appeared to inhibit. It was considered that the effects were caused by defect creation on solid solution, but it was acknowledged that the addition of vanadium aided sintering by liquid phase formation. Watson and Wilder (1960) found that 0.1% of vanadium pentoxide aided sintering of uranium dioxide, and claimed that the effect was due to interstitial solid solution at the surface of the particles below the melting point of the eutectic. -56-

Ilda and Ozaki (1959) found that while sintering of nickel oxide was enhanced by additions of calcium oxide, it was inhibited by sodium oxide, and especially by ferric oxide and alumina, while eerie oxide and silver oxide had no effect. It was also found that boric oxide enhanced grain growth, but it inhibited sintering. Nickel oxide derived from the sulphate showed greater grain growth than other samples. Iida and Ozaki (1961) found that grain growth in titania was enhanced by the addition of nickel oxide, cobaltous oxide, manganese dioxide, ferric oxide, cupric oxide and especially molybdenum trioxide, while chromic oxide promoted somewhat, and sodium oxide and tungsten trioxide had no effect.

Hopkins (1959) reported that ferric oxide, indium oxide and titanium dioxide promoted magnesia sintering, explained by solid solution and possibly lattice strain in some cases. Other oxides (chromic oxide, alumina, gallium oxide, stannic oxide) inhibited sintering, but it may be observed that there was measurable, and sometimes considerable, enhancement of sintering for certain small concentrations of additive, 0.01 - 0.2 mole*%, and that at lower temperatures the maximum enhancement is for larger concentrations of additive,

Kriek, Ford and White (1959) showed that titanium dioxide, silica, and alumina exhibited an optimum concentration for sintering enhancement, and suggested that this might be due to the formation of a spinel or silicate with much larger lattice parameters than magnesia, and thus the same effect is not observed with iron oxide, where there is little expansion of the lattice. However, this becomes somewhat inconsistent when considering the fall-off rates for alumina and titania additions, as they are exactly opposite to the -57- relative expansion effects. Calcium oxide was found to inhibit magnesia sintering, an effect claimed to be due to the dispersion of the oxide between the particle contact points, hindering diffusion.

Pampuch (1960) observed that titanium dioxide, cobaltous oxide and manganous oxide promoted densification of beryllia, and Aitken (1960, 1961) found that chromic oxide, nickel oxide and especially alumina and magnesia enhanced beryllia sintering_ even 0.25 0 of magnesia having a marked effect.

Poluboyarinov et al. (1962) also reported the enhancement of magnesia sintering by alumina, ferric oxide and especially titanium dioxide, while zirconium dioxide had different effects on magnesia prepared by different methods. Budnikov et al. (1965) found that hafnium dioxide enhanced magnesia sintering.

Ota (1961), in a series of papers on sintering studies on dead-burned sea-water magnesia, reported that the effect of additions of calcium oxide, silica and ferric oxide depended on the molar ratios CaO:SiO and CaO:Fe 0 Radio-isotopic 45 2 2 3. diffusion studies ( Ca and 5 Fe) showed that the diffusion rate for calcium was greatest for the molar ratio CaO:Si0 2 = 1, though monotonically increasing diffusion rates were observed when ferric oxide and alumina were also added. Titanium dioxide, chromic oxide manganese dioxide and boric oxide also increased diffusion. The effects observed were claimed to be due to liquid phase formation. It may be noted that the starting material was far from pure.

Ivanov (1962) found increased sintering and grain growth rates when fluoride was added to magnesium oxide, an observation which may account partly for the accelerated grain growth of dense magnesium oxide reported by Leipold and Nielson (1966), whose otherwise quite pure magnesia contained -58-

a considerable amount of fluoride.

Brown (1963, 1965) showed that sintering of magnesium oxide was enhanced by the addition of small quantities (0.01 and 0.1 cation-%) of-vanadium pentoxide. The derived activation energy for sintering was identical to that for pure magnesium oxide.

Wuensch and Vasilos (1966) indicated that the preferential diffusion of transition metal ions along grain boundaries was not observed when the usual contaminants, calcium oxide, silica and ferric oxide were not segregated at grain boundaries. Readey (1966) indicated that the effect of impurities on sintering might be explained in terms of the chemical potentials set up by the impurities.

Brophy et al.(1963) considered that the enhancement of tungsten sintering by additions of various platinum metals was due to accelerated grain boundary diffusion.

Many other observations of the effects of impurities on the sintering of various oxides are to hand; thus Smothers and Reynolds (1954), Cahoon and Christensen (1956) and Bagley (1964) found that alumina sintering was aided by ferric oxide, manganous oxide, cuprous oxide and titanium dioxide; Kukolev and Leve .(1955) reported enhancement by the order titanium dioxide>ferric oxide>manganese dioxide. Hijikata and Miyake (1960) reported enhancement by magnesium oxide, while Kato et al. (1965) reported that titanium dioxide, magnesia, cabalto-cobaltic oxide and especially manganese dioxide aided alumina sintering. BritSch (1959) found that more than 2% of sodium oxide was detrimental to alumina, by leading to idiomorphic grain growth, while Degtyareva and Kainarskii (1964) reported that titania, and magnesium, aluminium and zirconium titanates enhanced alumina zintering, and reduced the activation energy from 118 to 58-87 Kcal/mole, and Keski - 59 -

and Cutler (1965) found that up to 4% of manganous oxide increased alumina sintering, and proposed a volume diffusion mechanism.

Cutler et al.(1957) used mixed additions of manganous oxide-titanium dioxide, and cuprous oxide-titanium dioxide, and found that satisfactory densification at 1300- 1400°C. could be attained by adding L of such combinations to alumina, the optimum effect being for MnO:T102 = 58:42. Liquid-phase sintering appeared to have occurred, and grain growth was idiomorphic.

Formation of a liquid phase does not always promote sintering, as can be observed from the work of Hummel and Tien (1959), who showed that titanium oxide doped with 1 mole-% of lithium oxide did not densify at temperatures where the undoped oxide densified almost completely.

Knudsen et al. (1964) and Arthur and Scott (1964) showed that uranium oxide sintering was enhanced by titanium dioxide additions, without the liquid phase, and Ang and Burkhammer (1960) reported that both calcium oxide and titanium dioxide enhanced urania sintering.

1.3. (d) The Effect of Atmospheres.

While it was not expected that oxidising or reducing atmospheres would affect the sintering of normally stoi- &Diametric oxides like magnesium oxide, the work of Wertz et al. (1964) showed that some point defects were caused by heating magnesium oxide in hydrogen. For oxides with a tendency towards non-stoicheiometry, it was expected that appreciable differences would arise by sintering in different atmospheres. -6o-

Budnikov and Tresvyatskii (1954) ascribed the enhanced sintering of chromic oxide in oxygen to the formation of chromium trioxide. Williams et al. (1957) found that an increase in the oxygen partial pressure resulted in increased sintering 4+ rates in uranium dioxide, despite the fact that U is acknowledged to be the slower moving ion, while Ogura et al. (1963) found vacuum sintering of uranium dioxide to be preferential to hydrogen sintering in the intermediate stage, and suggested thatcloaning of the surface aided sintering. Amato et al. (1963, 1964) found that the sintering of uranium oxide was enhanced by using hydrogen or steam atmospheres, and claimed the effect was due to varying stoicheiometry.

Roberts, Hutchings and Wheeler (1956) and Roberts and Hutchings (1959) found that different samples of zinc oxide showed opposite effects, on sintering, of increasing the oxygen partial pressure; enhancement (more common) was. ascribed to chemisorption of oxygen (a view shared by Kuczynski, 1962 ), whereas inhibition was ascribed to a reduction of the interstitial zinc concentration. Norris and Parravano (1963) found'sintering of zinc oxide single crystals to take place by evaporation-condensation, and although there was rate dependence on the total ambient pressure (rate a 1 for p = 0.003-0.75 atm.) no conclusion could be drawn about the effect of oxygen partial pressure.

0!Bryan and Parravano (1962) concluded that the increased sinterability of reduced rutile could be explained by a defect structure.

Sandford and Ericsson (1958) found that water-vapour caused loss of oxygen on sintering alumina, but nitrogen had no effect. Coble (1962) found no difference in the intermediate stage sintering of alumina in hydrogen, nitrogen or oxygen, but when sintering had proceeded to the closed-pore stage the remaining porosity could only be eliminated if discontinuous -61-

grain growth did not occur, and if the sintering atmosphere was hydrogen, oxygen or a vacuum. Oishi and Hashimoto (1963) reported enhanced grain growth in alumina sintered in hydrogen, and explained this by enhanced diffusion due to an increase in the oxygen vacancy concentration.

1.3. (e) The Effect of Water - vapour on sintering of Oxides. Dell and Weller (1959) suggested that low temperature sintering of magnesium oxide was due to surface diffusion brought about by water adsorption, while Anderson and Horlock (1962) found that a thin layer of fine magnesium oxide powder did not decrease in surface area on heating to 1000°C. in vacuo, while larger samples showed pronounced surface area reduction, these effects being attributed to the presence of adsorbed water. Anderson and Morgan (1964) used a decomposed magnesium hydroxide powder with "30% monolayer hydroxyl coverage, consisting of 75A cubes of magnesium oxide in pseudomorphic remnants of magnesium hydroxide. Sintering and grain growth (to crystals -250A across) occurred in very low water vapour pressures (45 mm Hg) at temperatures above 400°C. At 1050°C, considerable reduction in the surface area occurred, and was thought to occur either by bridging between adjacent crystals across a micropore, or by net anion movement due to successive adsorption and desorption of water vapour. It was pointed out that the water vapour taking part in this sintering reaction was in a different environment from water molecules which had yet to be desorbed, and the latter probably do not take part in the sintering, unless they are first desorbed into the ambient atmosphere. These observations are in keeping with the findings of Hyde and Duckworth (1962) that water-vapour decreases densification. Aitken (1960) found beryllia sintering to be similarly retarded by water vapour. - 62 -

Eastman and Cutler (1966) indidated that at 800-1000°C. initial sintering of magnesia occurred by a grain boundary vacancy diffusion mechanism, with Mg++ as the slower ion. The rate of sintering increased with increasing partial pressure of water vapour, and it was claimed that water dissolved to form hydroxide, raising the cation vacancy concentration. The grain boundary diffusion coefficient, D obeyed the relation D ocpH Oi for ~ p (5mm Hg, and Dg at pH n0g 2 , n 1.0-1.5 for p>5mm Hg, with activation energies of densification 80 and 48 Kcal/mole, respectively. Apart from the effect of water-vapour during sintering of magnesium oxide, any water vapour attacking the oxide at room temperature will affect the sintering because of changing the surface condition of the oxide when the water is desorbed. In view of this, the effect of water and water vapour is reviewed here, and some preliminary experiments were conducted on the material used in the sintering experiments.

1.4. HYDRATION OF MAGNESIUM OXIDE.

Livey et al.(1957) and Morgan (1963) reported that not more than about a monomolecular layer of water is adsorbed from the atmosphere by magnesium oxide, produced from the hydroxide and basic carbonate respectively.Iayden (1961) and Leyden and Brindley (1963) suggested that water vapour attacked magnesia by adsorption followed by an interface reaction at nuclei, which was negligibly slow below about 30% relative humidity, and the rate of which appeared to be governed according to the function - 1) where (P/P* p = relative water vapour pressure, p*,-J0.3 p sat.. Below about 30% r.h. hydration was by a slow solid-state process.

Chown and Deacon (1964) found the rate of formation of magnesium hydroxide, in hydration of magnesia by water vapour, was very dependent on surface area, and that the reaction appeared -63..

to occur by capillary condensation in pores and subsequent reaction‘ Coleman and Ford (1964) found a first-order reaction in magnesium hydroxide formation, and a dependence on the surface area of micropores in the magnesia particles, again suggesting capillary condensation.

Schreiner (1952) studied the attack of water vapour on various calcined commercial magnesites, and found attack at some grain boundaries which caused swelling at the lIcentres of hydrationit which caused the bricks to fail. Rates of hydration were found not to correlate with ability of the magnesia to adsorb water vapour. The compound at the grain boundary showed a gradual change in structure from the periclaso (Mg0) structure to that of brucite (Mg(OH)2), with the broad, weak lines on the X-ray powder photographs characteristic of compounds which are not well crystallised, a finding which has been confirmed by later workers, and is also found for the dehydration of brucite. Adsorption isotherms for water adsorption show a partially irreversible hydration.

Razouk and Mikhail (1955, 1958) studied various samples of magnesia produced by calcining brucite and magnesite (MgCO3). The oxide was suspended in a sorption balance and the partial pressure of water vapour (at 35°C,) was raised every 24 hours, this time, it was claimed, being sufficient to attain equilibrium. Again, a partially irreversible hydration was observed, as shown in Fig. 1.2a. A sigmoidal curve in the plot of moles of water taken up versus partial pressure of water vapour was found, and the actual amount of water taken up varied with the calcination temperature, being less for a higher temperature of calcination, as shown in Fig. 1.2b. This falling-off of hydration tendencies with increasing calcination temperature, also reported — 64 —

Fig.1.212 Water Vapour Sorption on flglib Effect of Calcination Temper- Me gnes la. ature on Sorption on Magnesia. 1.0

0* • 02 0•4 04 0'6 10 0 0.2 04 06 09 1.0 PARTIAL PRESSURE OF WATER VAPOUR .%I p (Po • SAT. V. P. at 35°C.) •

Fig,1.3 infra-red Spectra of Maanesiurn Oxide and Magnesium Hydroxide. (Razouk and Mikhall,1958).

MI(OH)1 Hydrated M30 BRUCI TE

0 after dehydration Fresh undried of Brucite (OH)t rehydration 4 441rAltatial Hydrated MIO after °taigas sing rated at R .T. g° • 4000 3600 3200 3600 3200 2800 WAVENUMBERS [C MI WAVENUMBERS [CM] -65-

by Colegrave, Richardson and Rigby (1949), Budnikov and Voroblev (1959), and others has been correlated with decrease in surface area by Razouk and Mikhail (1959), Poluboyarinov et al. (1961), and others.

In an infra-red spectrophotometric study of the products of decomposition of brucite and magnesite, their hydration, and subsequent dehydration in vacuo at room temperature, Razouk and Mikhail (1958) reported a sharp band at 3782 -1 cm for natural brucite and prepared magnesium hydroxide, —1 a shoulder at 3782 cm for magnesia produced by dehydration of brucite, for the same material rehydrated, and a somewhat less distinct shoulder after a further dehydration. In all the specimens in which the peak or shoulder occurred it was followed at lower wave-numbers by a broad band extending -1 down to 3200 cm or less.

Fresh undried magnesium hydroxide showed a band at 3700 1 1 cilT followed by a broad stronger band at 3700-3200 cm , as did hydrated magnesia derived from magnesite, and also hydrated magnesia from the same source which had been out- gassed at room temperature. The spectra are shown in Fig.1.3.

Webster, Jones and Anderson (1965) reported that mag- o nesium hydroxide decomposed at 300 C. gave magnesium oxide exhibiting a sharp band at 3710 cm 1 which was converted in about 10 hours to oxide with ',normal hydrated surface!' 1 1 bands at 3752 cm and 3610 cm . The normal hydrated surface here referred to the surface which, when it had adsorbed less than a monolayer of water, had the water adsorbed as groups of five or six pairs of hydroxyl ions, as determined by measurement of second moments in N.E.R. 1 studies. The oxide with the 3710 cm band had a higher second moment, suggesting a closer approach of the protons -66-

in the hydroxyl groups to each other than in the ',normal hydrated surface l%

It was also found that the physi-sorbed water on the surface of the magnesium oxide slowly became converted to a more strongly bound species. A similar phenomenon was reported by Brey and Lawson (1964) for physisorbed water on thorium oxide, which they ascribed to diffusion to less accessible adsorption sites. They also reported that the interaction of water with thorium oxide prepared by heating the oxalate was less than that with the oxide prepared from the hydroxide. Nevertheless, the lowest coverage of water reported was just less than two layers, adsorption of seven layers was frequent, and up to 16 layers were also found.

1.5. GRAIN GROWTH. (a) Introduction and Early Observations.

Grains grow at the expense of other grains, the driving force for the process being the reduction in grain boundary area so obtained, and it has been established that in normal grain growth the process by which it occurs is the migration of curved grain boundaries towards their centres of curvature. The boundaries are curved because of the requirement for balance of grain boundary tensions at the grain edges in an irregular array of grains.

The early work on grain growth was with metals, and there are some differences between metals and sintered metal oxides in their grain growth characteristics, notably recrystallisation in metals, and the presence of porosity in sintered ceramics.

'Recrystallisationll is the form of grain growth in metals which consists of the formation and growth of nuclei in a matrix which has been strained by cold-work. The driving -67-

force is the strain erergy stored in the strained matrix. The growth of recrystallisation nuclei is controlled by the local conditions, and there is not the same obvious control by surface tension as in normal grain growth.

Beck and Sperry (1950) noted that in recrystallisation the boundaries migrate away from their centres of curvature, the opposite direction from normal grain growth. The course of recrystallisation was observed by successive heating and etching of a sheet of aluminium, giving concentric rings round a nucleus in a grain, and successive semicircular rings radiating from grain boundary nucleation. The less-strained specimens always grew by the latter mechanism, with the new strain-free grains having the same orientation as the strained crystals. Recrystallisation obeyed the D = grain size relation D = kt. k = constant t = time Beck, Kremer and Demer (1947) found that isothermal n grain growth in aluminium obeyed the relation D = kt , where n (isothermally constant) varied from 0.06 at 350 C. to 0.16 at 500°C., with a linear increase between these temperatures, provided that the grain size did not approach the specimen thickness (as the grain growth then stopped, with grain boundaries perpendicular to the surface). It was pointed out that a strictly rigorous derivation of an activation energy was impossible, as k is not a rate constant because of the variability of n. Nevertheless, a temperature dependence (55-65 Kcal/mole) was derived by taking D = D (t exp )n at constant time for the o RT range of grain sizes observed. As this was higher than the reported activation energy for self-diffusion in aluminium, it was suggested that this might mean a grain- boundary diffusion activation energy higher than the self- -68

diffusion activation energy. It is unfortunate that later workers derived activation energies in a similar manner without the caution of Beck et al.(1947) as to their significance.. Beck, Towers. and Manly (1948) found that n was almost independent of temperature for a - brass.

Beck, Kremer et al.(1948) noted that ',discontinuous grain growths', the growth of large crystals embedded in a matrix of smaller ones, occurred in some copper-beryllium alloys to which impurities had been added, and also noted the specimen thickness effect, with small surface grains covering larger bulk ones. Burke and Shiau (1948) also observed that grain growth was inhibited by the surface, and showed that the grain growth rate was dependent on both grain size and temperature.

Beck (1948) derived the relation D'4 - Ct, where both n and C depend on temperature, and Do = recrystallised grain size: Burke (1949) predicted the same relation from the consideration of boundaries moving towards their centres of curvature in an attempt to reduce the grain boundary area. The rate of boundary migration was expected to be proportional to the curvature of the boundary, and this should, over the whole specimen, give a grain growth rate proportional to the reciprocal of the instantaneous grain size (for normal grain 1 2 growth). -- DdD/dt, thus D - D 2 = kt. This relation dtdDc D' o will hold only if the grain size distribution and average interfacial energy remain constant. The constant k should be temperature dependent according to the expression k = Ae—Q/ RT" A relation was also derived for grain growth to a limiting grain size Df, which, for grain growth in brass, -69-

was. obeyed for shorter times, but deviated from at longer d times. It was taken that D 1 1 --dt = K(—D - D—)' and this was D -D f integrated to o + , nk D -D —7K .i f f oN t. Zenerts relation D ------D -D)- D 4 f f f D = r r = radius of inclusion f f' f = volume fraction of inclusions' quotas' by Smith (1948), was considered, but it was pointed out that in the fast initial grain growth the grain boundaries might well migrate so fast that the inclusions 7zu loft behind; grain growth is, in fast, expected to occur in jumps, as fast migration is likely when the local equilibrium of the grain boundary is disturbed on the formation of local, unstable geometries during the absorption of a grain. The diffusion of soluble impurities to grain boundaries would have the same effect of lowering grain growth rates with time, as would a surface tension decrease due to closer orientation of adjacent lattices.

The average radius of curvature may increase faster than the average grain size, owing to approach of interfacial angles to the 1200 observed in plane section, and any variation in the grain size distribution must also be taken into account.

McCrone and Cheng (1949) reported that normal grain growth in octachloropropane, chosen for its convenience in observation, appeared to obey a growth law D = Kt, though Beck (1949) considered that the range of values of D used (0.012 - 0.01710 was too small for accurate determination, and the data appeared to fit a curve D=Ktn, n<1. Turkalo and Turnbull (1949) reported that discontinuous grain growth in copper obeyed the relation Dan. - 70-

1.5. (b) The Importance of Crystallographic Orientation.

It was observed by Beck and Hu (1949) that grains nucleated by scratching the surface of rolled aluminium recrystallise preferentially at an angle of 30-50° to the[11l] direction of the rolled crystal, and the same preferred growth, or possibly, though less likely preferred nucleation, was reported by Beck and Sperry (1949). Beck, Towers and Sperry (1949), and Kronberg and Wilson (1949) reported a Ylcuben structure in some copper samples, in which adjacent grains were clearly oriented at 90° to each other, especially for metal which had been greatly reduced by rolling.

Dunn (1949) found a method of preparing three-grain specimens of metals, with selected relative orientations, and Dunn and Lionetti (1949) allowed such specimens (of silicon- iron) to reach equilibrium angles by notching the edge of the plate to anchor the end of the grain boundary. By maintaining one relative orientation constant, the relative grain boundary energy for different relative orientations was obtained for (110) planes. The relative grain boundary energy rose from a very small value for small mismatch to a maximum between 20° and 30°, decreasing to a saddle-point at about 70°, and increasing again to a peak at 90°, though still less than at 20-30° mismatch. Dunn, Lionetti and Bolton (1950) found that the energy of a L1121 twin in such a (110) plane sheet was 0.2 - 0.25 of the normal boundary energy, with the energy rising rapidly with increasing mismatch from the twin position.

The occurrence of Itannealing twins!! at grain edges, stabilised by a lower total boundary energy than there would be for an extension of the twinned grain to the edge, is a feature of grain growth in metals which has yet to be reported for grain growth in ionic crystals. -- 71-

1.5. (c) The Mechanisms of Grain Growth.

At the tine of the review of Beck (1954), there was still some question as to the correct form of expression of the dD 141 grain growth rate law. For the expression nCD1 n was given as 0.5 for brass at all temperatures, and for 0 aluminium n350o = 0.056, n600oc. = 0.322, nm.p. f-A0.5 2 were the values quoted. The expression D - Dot = Ct, which could be better justified theoretically, is identical to the above expression for n=0.5. Two forms of grain growth were recognisedt (a) ngradualo or #normalm grain grain growth where there is an increase ii grain size without a substantial change in the grain size distribution, and (b) '!.secondary reorystallisationp, qabnormalP or ldiscontinu- oustf-grain growth, or 4coarsening!*, where a few large grains grow among a matrix of smaller crystals, forming a Ilduplexl! structures.

Discontinuous grain growth was thought to occur because of dispersed second phase, inhibiting grain boundary motion, or perhaps a closeness of relative orientation giving low mobility to most grains, with a few growing more-misoriented grains.

Normal grain growth could, in the absence of factors leading to discontinuous grain growth, only be stopped by formation of an array of perfedtly stacked tetrakaidecahedra throughout the sample, or the formation of a single crystal, and as the former case never arises in practice, the grain growth may be expected to continue to give a single crystal, though when the grains are large, grain growth is slow, and may eventually be stopped by other factors, such as inclusions, or the specimen thickness effect. -72-

It was accepted that the mechanism of grain boundary migration was the transfer of atoms from the convex side of the boundary to the concave side. A certain quantity of energy is required to activate an atom or group of atoms sufficiently to leave its ionic environment on the convex side, but on fitting into the other side of the boundary a slightly greater amount of energy will be released. At any temperature above absolute zero this activation energy will be possessed by some of the atons.or groups, with the number increasing with increasing temperature. The difference in free energy between the two sides of the boundary is due to the difference in curvature. Turn- bull (1951) suggested that the activation energy for grain growth should equal that for grain boundary diffusion. It shoUld be 'borne in mind that there was at the time a controversy as to the nature of a grain boundary, the choices being (a) an flamorphous cement!' many atomic layers thick, (b) numerous disordered blocks or groups of atoms (K1, 1949). 1 and (c) an abrupt transition between the two lattices. Only for (c) would the activation energy required to diffuse atoms along the grain boudary equal that for diffusion across .it.

Greenwood (1956) pointed out that for solute particles in a saturated solution, smaller particles would dissolve and larger ones grow, according to the relation D3 - Doi = 3 S Mit, where D1=diffusivity in solution, D1 RT p S=solubility, M=molecular wt./o'=density. It was found that the relation was obeyed, to within an order of mag, nitude, for U-Pb and U-Na slurries.

Feltham (1957) found that grain sizes and shapes in metals were lognormally distributed in planar sections, -73-

and the distribution was found to be constant during grain growth. From this it was proposed that the relation 2 D Dot = K oexp (-H) t should hold for Metals. Feltham RT and Copley (1958) confirmed that this relation held for a-brass, if an adjustment was made to the exponential term for the effect of the presence of zinc.

Levesque, Gerlach and Zneimer (1958) studied grain growth in nickel ferrite, and fitted the data to the relation n D=D t where D 1 ' 1= grain size after 1 grain size, n isothermally constant. n varied from 0.2 (1300°C.) to 0.39 (1400°C.) and an activation energy of 90 Kcal/mole was derived.

1.5. (d) The Effect of Inclusions.

Burke (1957 a,b) demonstrated the manner in which inclusions may retard grain boundary migration in metals, and extended the treatment to oxides, with the pores between the grains acting as inclusions. Using the relation D =d, and the observation that the average pore size is f T about one tenth of the average grain size of the matrix of a duplex structurep,ir = f = 0.1, i.e. discontinuous grain f growth would occur at 10,g porosity, and the limiting density would be about 900, as when discontinuous grain growth occurs pores are isolated from grain boundaries. This relation assumed an even distribution of pores, accept in a few place's where discontinuous grain growth began.

The relation — = f deservescloSer examination than it D f has been given hitherto. Though d.D.1 Df has been observed, it is doubtful whether an array of such pores - 74 -

entirely on grain boundaries would give 10% porosity, as this would require an average of 100 pores per grain, whereas published photomicrographs of duplex structures usually show one or two, and certainly never more than about four pores in plane section of a grain. It is hardly conceivable that this could be equivalent, in the bulk of the solid mass, to 100 pores per grain, especially when it is considered that each face is shared with another grain, aid each edge with two others. It is more likely that there are about ten pores per grain. Thus, though there is definitely a relation between the incidence of pores and grain growth inhibition, it is doubtful whether the - = f relation is a satisfactory representation of it. Haman° and Kinoshita (1964) reported an attempt to derive a relation between grain growth and pore and grain sizes.

1.5. (e) Work with Pure Metals.

Bolling and Winegard (1958a) studied the grain growth of zone-refined lead and found that an empirical relation- n ship D = At (n = 0.4) applied for the highest temperature used. A limiting grain size was observed, and the data D were fitted to the relation - + in ( K t D ) = -7 (i.e. f D f Burkels relation(1949) with D0=0), though it was not known whether the limiting grain size was due to inclusions or the specimen thickness effect. With doubly-refined lead n had a value nearer 0.50. An activation energy of 6.7 Kcal/mole was obtained, compared' with 12 Kcal/mole for grain-boundary diffusion and 22 Kcal/mole for volume diffusion, though both the diffusion values had been - obtained with less pure lead. The grain growth activation energy is of doubtful significance in view of the method of determination. -75-

In studying the effect •of impurities on grain growth of zone-refined lead, Bolling and Winegard (1958b) found that the value of n varied with the impurity, from n=0.48 to n=0.57 for 0.005-0.040 of silver, and from n=0.56 to n=0.6 for 0.005-0.02% of gold. The derived.activntion energy increased by a factor of more than two owing to the additions, and the frequency factor also increased, by up to 105-fold. The value of the free energy change did not appear to vary much, however, between the pure and doped lead, and it was considered that the mechanism of grain growth was not substantially changed. The differences were claimed to be due to the grain boundary segregation of the solute, and the effect of this diminished to zero on heating to the melting-point. The effect of a greater comparative concentration at the boundary (compared with the bulk) was noted in the greater effect for the same percentage doping of gold than of silver, which was in turn greater than for tin.

Holmes and Winegard (1959) found the D a t4 law applied to grain growth in zone-refined tin, and suggested that their observations agreed with the liquid-like structure of grain boundaries proposed by K3 (1947).

1.5. (f). Theoretical Aspects.

LUcke and Deterte (1957) derived expressions for the absolute grain boundary migration rate, and other grain growth relations for grain growth in the presence of impurities segregated at the grain boundary, and concluded that at high solute concentrations and low temperatures the boundaries would be held back by the foreign atoms, while at higher temperatures breakaway might give rise to faster growth. -76-

Mullins (1958), assuming surface diffusion to be responsible for the surface grooving observed in metals, showed that it might well be fixing of the end of a grain boundary in a surface groove which stops grain growth, and gives rise to the specimen thickness effect. The grain boundary can break away only if it is so curved that a reduction in surface area will be achieved by this-means; this breakaway cannot occur if both ends are tied. It was shown that with copper specimens the motion of grain boundaries across the surface was spasmodic rather than continuous, with grain boundaries temporarily pinned in surface grooves.

1.5. (g) Grain Growth in Non-metals.

For metal oxides and other ionic compounds the investigation Of grain growth phenomena has been mainly qualitative, with some notable More recent exceptions.

Duwez, Odell and Taylor (1949) found that in the sintering of beryllium oxide the final grain size for sintered fine powder was much greater than that for coarser materials, so that in particles above a certain critical particle size, no grain growth appeared to take place. Smothers and Reynolds (1954) noted that additives to alumina affected its grain growth rate, and for grain growth enhancement it was suggested that in some cases solid solutions increased material transport by straining the lattice, while in other cases glassy phases appeared. Some additions retarded grain growth and this was attributed to the filling of anion vacancies, or the production of complex ions of impeded diffusion Characteristics. Cahoon and Christensen (1956) found that iron, titanium and manganese oxides promoted grain growth in alumina, while many other additives retarded grain growth - 77 -

(especially magnesium oxide and silica) or had no effect. An alumina powder containing 0.026/3 of magnesia failed to exhibit grain growth, and as little as 0.04% of nickel oxide inhibited grain growth. It should-be pointed out that the form of grain growth observed by Cahoon and Christensen was idiomorphic grain growth, in which the grain shapes are not controlled by surface tension balance, but adopt their normal crystal habit. The effect of larger quantities of additive in spheroidising the grains was accompanied by a change-over from enhancement to inhibition of grain growth. Another example of idiomorphic grain growth occurs in the columnar grains growing in sintered uranium oxide under certain conditions, observed by MacEwan and Lawson (1962). The existence of several types of grain growth in alumina, induCed by different additions, was reported as early as 1940 by Noda and Isihara.

The incorrect integrations in the presentation of the grain growth laws by Burke (1957, 1959) have caused some confusion, but the correctly integrated form appears in the review of Coble and Burke (1963).

It was shown by von Neumann' (1952) that the growth potential for any n-sided grain is proportional to (n-6), as this represents the curvature of the faces. If a powder compact is sintered with one large single-crystal particle in it, then when sintering has occurred to such a point that grain growth may take place, the large crystal grows at a much faster rate than the smaller particles, as all the particles touching it have contributed sides to the particle. This is shown to be so by Burke,(1957) and Denton and Murray (1959). If, in a powder compact generally prevented from growth by inclusions or pores, there is a grain which by chance -78-

is less inhibited, then this grain will grow, consuming other grains and adding sides, so that it may form one grain from a thousand or so of the matrix grains. This process often occurs so quickly that pores are isolated inside the discontinuous grain,-giving material which is not fully dense. Coble (1961) showed that additions of magnesia to alumina inhibit discontinuous grain growth, allowing sintering to occur up to theoretical density. It was argued that there was insufficient spinel second phase to inhibit by inclusions (Coble and Burke, 1963), and that if the inhibition was by grain boundary segregation, then any inhibition of grain boundary migration should lead to a slower grain growth rate for doped alumina than for the matrix growth of undoped alumina, whereas the grain growth rates appeared equal. It was thought that the magnesia might change pore shapes, or enhance sintering, or that the grain growth rate in alumina was controlled by pores, and the magnesia reduced the maximum rate of grain boundary migration, but only to a value comparable with the actual rate in porous alumina.

Even if discontinuous grain growth does:occur, densification may continue (Burke, 1957 a, b) as discontinuous grains grow until their growth is slowed, probably by impinging on other such grains, when they can grow by normal grain growth at the expense of the other discontinuous grains. The rate will be slow enough to sweep pores out of the path of the moving grain boundary, indeed, it will be impossible for the grains to grow without absorbing the pores in its path. The rate of this densification is extremely slow, and the specimen probably will not densify at a significant rate.

Amato (1965) proposed that discontinuous grain growth in uranium dioxide was caused by pores full of gas from the -79-

decompoSition of organic binders, while Elyard, Gibbs and Rawson (1963) suggested that the discontinuous grain growth could be prevented by addition of fine platinum • powder as a second phase, or by sintering for prolonged periods at temperatures lower than those usually used.

Belle and Lustman (1957) reported that the slope of logarithmic size vs. time plots for grain growth in uranium dioxide at 1500-17000C. gave an initial slope of -,0.67-0.9, whidh at 1700°C later decreased to 1

Lida (1958) found that, for nickel oxide, the relation n D l = Kt was obeyed, with n ,.11.8, the temperature dependence of K being represented by an #activation energy" (E) of 55 Kcal/mole. It was pointed out that Ni++ ions are rate-controlling in oxidation of nickel with E = 41 Kcal/mole. The atmosphere appeared to affect grain growth rates, and heating in air gave rounded grains while triangular grains were observed in oxygen and argon, there being no grain growth when nickel oxide was heated in vacuo As the pressure of oxygen had no effect on grain growth, it was claimed that vacancy theories did not reasonably account for this process.

Felten (1961) reported that, for beryllium oxide, D a t initially, ascribed to discontinuous grain growth, followed by decrease to D3 a t for normal grain growth. This one-third power time-dependence was also reported by Coble (1961) for normal grain growth in doped alumina, Coble drew attention to the similarity between the activation energies for grain growth and sintering in alumina, and suggested that grain growth might be controlled by pore removal rates. 8o

Cutler (1959) studied the probably discontinuous grain growth of alumina by meaUrim the ten largest grains in a thin section of sintered material. Logarithmic plots of size vs. time gave straight lines, with a derived activation energy of 160 Kcal/mole. For refired alumina _an activation energy of 170 Kcal/mole was derived, suggesting that there was little difference in the activation energy for somewhat different porosities. There was no grain growth below 80% dense. It was suggested that the high value for the activation energy was due to the requirement of a pure material to create vacancies as well as move them, while in a less pure material the vacancies may be created by the addition of altervalent ions.

Thus, Mott and Gurney (1940) gave E = U + E = process activation energy - ,while EtZe1 and Maurer (1950) U = movement W = vacancy pair formation energy found that small concentrations of cadmium chloride added to sodium chloride introduced a large number of vacancies, so that might be considered negligible for such doped materials, 2 and hence

Daniels et al. (1962) reported that the grain growth relation D2 = Kt held for magnesium and calcium oxides, with derived activation energies of 60 and 110 Kcal/mole respectively. It was also reported that the grain growth relation was unaffected by varying porosity. Examination of their. data reveals a drop in the time exponent to ,-,0.43 for long periods of sintering.

MacEwan (1962) reported that grain growth in uranium 2 dioxide followed the relation D - D ot = k t0'8 where - k = k exp , 8']R00): o T -81-

AMato, Colombo and Protti (1963) expressed the grain growth relation for uranium dioxide in the form D2 - Dot = n k t , and found that for hydrogen sintering n = 0.93 + 0.15, and for sintering in carbon dioxide n = 0.77 + 0.12, with derived activation energies of 46-50 Kcal/mole. Other workers had given values for n of 0.8, 0.9 and 1.2. Coble and Burke (1961) remarked on the difficulties in the interpretation of results reported in the literature because of the unknown impurity contents and the unknown effect of impurities. Nicholson (1963) showed that for additions of 0.1 cation-% of vanadium there was a great enhancement of grain growth rate, due to the formation of a liquid phase. For magnesium oxide doped with up to 2% of vanadium, the growth rate law D3 = kt was observed, while doping with 1 cation-% of titanium gave D3 = kt, E = 104 + 20 Kcal, compared with an activation energy of 62 Kcal/mole 4 for the vanadium-doped magnesia. 1% of iron gave D = kt, E = 146 + 25 Kcal/mole. For both titanium and iron doping solid solutions were formed, and in addition the titanium doped material contained some Mg2TiO4. The importance of small quantities of additives in grain growth may be judged by the work of LOckel Deterte and co- workers, summarised by Lucke and Deterte (1957), in which it was found that 0.01% of manganese or iron inhibited recrystal- 12 16 lisation of aluminium by factors of 10 and 10 respectively. It appeared that smaller quantities had much less than a proportional effect. Grain boundary solute segregation was' thought to be responsible for the effect. D3 - Doi = k exp Stehle (1963) reported the relation o (-87000 k 1550-2100°C., -----)tRT for grain growth in uranium dioxide at while Tien and Subbarao (1963) found that grain growth in Ca0.16Zr 0.840 1.84 could be represented by D = ktn, where n - 82-

decreased from 0.41 at 1600°C. to 0.32 at 2000°C. An activation energy of 80 Kcal/mole was derived, possibly rising as high as 91 Kcal/mole when the change in n was considered. lv fA Bruch (1962) found that while the D t ' law described the grain growth of interior grains, the grains at the surface of the specimen appeared to obey the lair D a 01, while Clare (1966) also reported a D a 0 law for the growth of interior grains in beryllium oxide, with E=104 Kcal/mole. Felten (1961) showed that for grain growth in beryllium oxide doped with 0.1% (molar) of various additives, the largest grain sizes were given by beryllia doped with titanium dioxide, calcium oxide and strontium oxide, all of which form a liquid phase with beryllia at the temperature used, 1700°C. Bannister (1964) reported that grain growth in beryllium oxide obeyed the relation D = kt0*45 for D = 1.5-1511. Buist et al.(1965) reported that grain growth in magnesia, calcium oxide and alumina in the presence of a liquid phase obeyed the relation D a tY3 found by Nicholson (1963) for liquid phase participation in growth.

Duderstadt and White (1965) reported D = ktn, n 4w0.3 for beryllia doped with 0.5% of magnesia or 3% of zirconium dioxide, and Haertling (1966) found D = kt"3 for grain growth in hot-pressed lead zirconate and titanate with bismuth 3-D 3 additions, while Lyons et al. (1963) found D o =kt for U02.

1.5. (h) The Effect of Grain Boundaries and Pores on Grain Growth. Jorgensen and Westbrook (1964) showed that the micro- hardness, determined by conventional indentation techniques, may be used to determine the solute distribution in a solid - 83 -

solution. It was found that addition of magnesia to alumina resulted in only a small increase in the bulk hardness, but the grain boundary hardness increased quickly, levelling off to a constant value for more than about 0.8 wt.-% magnesia. However, at the highest temperatures used there was no measurable difference between the bulk and grain boundary hardness, though discontinuous grain growth was still prevented by the magnesia. Other oxides were found to have a similar segregating effect, and there was a correlation between the sintered density reached and the relative grain boundary hardness, 'compared with the undoped sample.

Jorgensen (1965) found that for normal grain growth in alumina and magnesia-doped alumina the grain sizes for the undoped material were larger than for the other, contrary to the report of Coble (1961). It was deduced that the control of grain growth in alumina by magnesia was by means of solute segregation and not pore inhibition.

Sjodahl and Westbrook (1965) considered similar effects in magnesia-and calcium oxide-doped beryllium oxide to be due to the same phenomenon.

Kingery and Francois (1965) considered the pores on grain boundaries in porous compacts,and concluded that the pores must travel with the grain boundaries during grain growth. Material may be transported from one side of the pore to the other by evaporation-condensation, surface diffusion (see Barnes and Mazey, 1963) or volume diffusion. As the distance of transport is proportional to the pore size, the rate of pore migration was expected to be inversely proportional to the pore diameter. If pore growth is such K Kfl, whence that dpaD, it was claimed that --dt = D 47 - K2 Kit p D or Dats' if D D3-Do 3 t, o<

that the grain growth activation energy should be identical to the sintering activation energy-for porous compacts. Speight and Greenwood (1964) also considered the problem of the retarding effect of pores on grain growth,, and showed that'the pores will break away from the grain boundary for a critical value of Q - Q Qb = grain boundary activation energy b s Q If s = surface for diffusion 7 and any relations derived for grain boundary migrations under such conditions will involve the activation energies of both grain boundary and surface diffusion.

Patrick and Cutler (1965) sintered mixtures of large and small particles of the same pure alumina material,and found the grain growth relation Dn = kt, with n varying from 5.1 to 7,7. It was found that the value of k was greater for the larger particles than for the smaller oneS, Even with this apparent grain growth enhancement for larger particles, the effect was insufficient to account for the very large grains found on grain growth at low temperatures for short times.

Kooy (1962) suggested that idiomorphic grain growth might be explained by a larger surface tension for the large grains than for the matrix, but the suggestion of Bagley (1963) that impurities, especially sodium oxide, might account for such growth in alumina was considered by Patrick and Cutler to be more likely, though some confusion between discontinuous and idiomorphic grain growth still appears to exist.

Spriggs, Brissette and Vasilos (1964) studied grain growth in fully dense magnesium oxide, and concluded that the relation D = ktn, where n varied between 0.42 and 0.45, -85-

could be fitted to the data, and an activation energy of 80 + 10 Kcal/mole was derived. The actual grain growth rate was four to d.x times that reported for porous magnesium oxide, and it was deduced that porosity decreases the grain growth rate as well as limiting the grain size and decreasing the time exponent. It wasthought that impurities might well decrease the time exponent as well as porosity.

1.6.BROAD COUGLUSIONS FROM PREVIOUS WORK: FIELDS FOR FURTEFiR 4SEARCH.

It has been established that during sintering vacancy diffusion from pores to nearby grain boundary sinks, either by volume diffusion or grain boundary diffusion, provides a major contribution to densification.

The intermediate stage of sintering has been described by a model (Coble, 1961) which has not been fully substantiated because of the lack of measurements of simultaneous grain growth rates. As the semilogarithmic relationship relies on a one-third power time dependence of grain growth, and in view of the interrelation of sintering, diffusion and grain growth activation energies (Morgan, 1963) which would result if the model were correct, simultaneous measurements of sintering and grain growth were essential for substan- tiation of the model.

Most of the previous work has been carried out on commercial materials, and although this has led to conclusions useful in the manufacture of comparatively pure refractory oxide components, the level of impurities has precluded the determination of the intrinsic properties of the oxides. A full knowledge of the intrinsic sintering and grain growth properties of an oxide with known particle size and shape -86-

is essential before the effects of small quantities of additives can be accurately determined, and thus an estimate made of the properties of any given oxide of known impurity content.

In previous work on the sintering of magnesium oxide powders, few details of the extent of hydration of the material used have been given. In view of both the possible low temperature sintering of magnesium oxide in the presence of water vapour, and the possible surface modification on desorption , it is essential to determine the water content and distribution.

Magnesium oxide provided a useful material for investigation, as the simple crystal structure, known ionic self-diffusion coefficients, and some previous work on the sintering of both impure and purer materials provided a basis for the interpretation of the sintering and grain growth phenomena, and the possible applications of pure magnesia as a refractory material (Boles, 1962) provided an incentive for further investigation of the sintering properties of the oxide. - 87 -

.CHAPTER_2,

Experimental Techniques.

2.1. Furnace Equipment 88 (a)"Nichrome V" wound Furnaces (b)Silicon Carbide Furnaces (c)Molybdenum wound Furnace

2.2. Temperature Measurement 94

2.3. Preparation of Specimens 96 (a)The Use of Binders (b)Pelleting Procedure

2.4. Density Measurement 97 (a)Micrometer Screw Gauge (b)Mercury Displacement Hydrometer

2.5. Polishing 99

2.6. Optical Microscopy 99

2.7. Infra-red Spectrophotometry 100

2.8. Other Techniques 100 - -

2.1. Furnrzce ;1,7uiprient.

Furnacet with three tyes of heating element were used: .7lichrome V'' silicon cerbide, and .:017bdenura.

(a) uNichr(yee T. wound Furnaces.

',Nichrome V is the alloy 80% Ni-20;; Cr, which may be used in air up to 1150°C. wire temperature. The practical temperature limit for a furnace wound with 'Tichrome Vn wire or tape is 1050°C., though 1100°C. may be used with care. A silica Pot, 12.'7 cm, in external diameter, 30.5 cm. deep, and with walls about 08 cm. thick, was wound with 35 turns of 'Tichrome IP' tape 3.2 x 0.8 u:A. A piece of heat-insulating brick was cut and placed in the bottom ,of the pot to give a floor at the same temperature as the walls in the hot zone. The wound pot was placed vertically on a bed of "M.I.23" heat-insulating bricks, and surrounded by shaped bricks of the same material, and all was enclosed in a "Sindanyo" box. Manual control over the temperature of the furnace was maintained by the use of e model 50B 'Wariac', auto-transformer as the power supply. The top baffle consisted of a brick cut cylindrically to fit into the top of the pot, with a collar for support, and a groove cut for insertion of a thermocouple into the furnace . Another furnace, constructed similarly, but with a horizontal rectangular chamber 28 x 12 x 9 cm. as its working volume, was also used, end was similarly manually controlled and supelied by a ''Variacl auto-transformer.

W Silicon Carbide Furnaces.

A muff le furnace with a 25 x 25 x 15 cm. working chamber, and access by a 12 x 9 cm. port in one side, was heated by six "Crusilitel silicon carbide rods in the roof. The surfaces of the working chamber and insulation were provided by suitably shaped .'11.1.28" insulating bricks, and the supply of current to -89-

the rods, via a transformer of manually adjustable output, was governed by a temperature contoller manufactured by the Indust- rial Pyrometer Co. Ltd. Temperatures up to 1250°C. were attained, with control to ± 20°C. The furnace may, however, be used at temperatures up to 1350°C. A silicon carbide tube, 7.5 cm. in outside diameter, with a double helical slot giving a hot zone 16 cm. long, was the heating element of a furnace modelled on the Morgan Crucible Co. Ltd.'s T7 furnace. The tube was held vertical and surrounded by insulating bricks, and an alumina inner tube was supported con- centrically inside it. Access to the working zone was achieved by moving an alumina brick cylinder, whose upper surface formed the floor, to the to of the inner tube by means of a stainless stool rod manipulated from below, placing the charge, in a suitable container, on the top of the cylinder, and lowering it down into the hot zone of the furnace. A baffle consisting of a brick cut cylindrically for part of its length, the rest acting as a supporting collar, and with a groove cut in it for insertion of a thermocouple, was then placed in the top of the alumina tube. Temperature control was by means of an ;,Electroflo', temperature controller operated by a thermocouple embedded in the insulating brick near the hot zone of the silicon carbide tube. The current and voltage supplied to the furnace were controlled manually by a ,Wariac" auto-transformer. The furnace was used for temperatures up to 1450:iC., and the control was to within 10°C,

) MolybdenumwoundFurnace,

A PCA 10 "Pyrocore,' furnace, supplied by Metals esearch Ltd., was heated by a molybdenum wire which was protected from oxidation and recrystallisation by a constant flow of hydrogen The wire was wound round the outside of the pure, recrystallised alumina working tube for a length of 9 inches, and this - 90 -

was contained inside another alumina tube, with alumina chips occupying the intervening seace. The tubes were both sealed at the lower end, and the upper ends were fitted into a gas- tii:;ht water-cooled netal header. The inner tube was in' long and 1" inside diameter, while the outer tube was ITV long and 2":" inside diameter. The unit was assembled in a water-cooled

case about 6.5? in dianet3r, with alumina powdar in the intervening space. The hot zone of the furnace was about 4" long, and a tungsten/26 , rhenium-tungsten thermocouple was situated between the two tubes near the hot ;!,one. At the bottom of the tube 3,1 of alumina powder acted as a radiation stopper, and at the top 3" of alumina brick limited radiation losses. The furnace is illustrated in Fig. 2.1. The charge was handled in the furnace by placing it in an alumina crucible cemente t to an alumina rod. This rod, and another, which was attached to the baffle, were held in a chuck attached to the pinion of a vertically-mounted rack and pinion device. A platinum or platinum-rhodium wire basket formed around the crucible and tied to the rod ensured that the crucible did not fall to the bottb.. of the furnace if the cemented joint failed. The charge could be lowered into the hot zone by roving the chuck down to a predeterIned nark on the rack. The tem-cerature distribution in the hot, zone was cletermined by using a crucible containing a thermocouple embedded in magnesia powder. The furnace was fitted into a unit which contained all the equipment for temperature control and mesurement, and also the facilities for handling the charge. Temperature control was by means of a Manually operated "Variac autotransformer supplying current to the low-voltage transformer, whose output was — 91 — CHARGE P 0 WE TERMINALS

I I METAL HEADER

II II HEADER COOLING I I I I I I I I IYDROGEN IN I I I I II I II I I I II GLAND RI NG

W/W -26 %Re

••• • THERMOCOUPLE

INNER ALUMINA TUBE ttt WINDING

OUTER ALUMINA TUBE ,••• $11•11111.1.1•0

HYDROGEN OUT

OUTER CASE

COOLING PIPES

••••IMMIO .1.1•111. 01111=10 INSULAT I NG ALUM INA POWDER

BASE PLATE Flg.2.1 THE "PYROCORE" FURNACE. -92-

delivered to the furnace via a 40 amp. fuse; current and voltage were monitored. Safety devices were incorporated to switch off the furnace in the event of a reduction of hydrogen pressure or water -,3ressure below accepta;:de levels, and also a dev-. ice to prevent the furnace being switched on again after restoration of poIer following a power failure without first returning the "Variac" autotransformor to its. zero output level. This prevents excessive current being pased through the molybdenum windintpthen its resistance has been decreased by cooling down after/power failure. The circuit diagram is shown in Fig. 2.2. Copper tubing was used in all the gas and water connections, and regular checking for gas-tightness was carried out. Hyd- rogen gas was supplied from 110 Cu. ft. cylinders, and an auto- matic changeover of cylinders on exhaustion of one was effected by setting the reducing valve of the nearly exhausted cylinder to deliver a higher-pressure than the other, both being above the minimum acceptable limit. The gas was dried by passing through a column of Magnesiu:m.berchlorate ("Anhydrone") 10" long, delivered via the safety switch to a needle .valve, and supplied to the furnace. The exhaust gas was bubbled through silicone oil, with a reservoir in the bubbler to prevent suck- back of the oil into the furnace, and then vented to the outside atmosphere. The furnace 'la_ flushed with hydrogen overnight before switching on, and was further flushed at 100C for four hours before raising the temperature to the working range. The heating up to 1500°C. was performed gradually, over at least 24 hours. Variation in the mains voltage affected the stability of the temperature of the furnace, but it•did not vary by more than .1.0°C. The maximum temperature at which the furnace was used was 130G0C., and though the furnace may. be used a)ove CONTACTOR zcm..-7..=====4 L 15a LON VOLTAG211. E . .J1 0 TRANSFORMER a it N ,I Mains MAINS SW ITCH (!; as' FURNACE

OFF II I I I ii I II ON — sprinq- baled to open -circuit. srinq -boded to 11 c Iosed-circuit. il tat L. Fig. 2.2 PYROCORE FURNACE : - WIRING DIAGRAM

GAS PRESSURE water WATER PRESSURE -94-

this temperature, its life would be considerably shortened. The operating limitations are imposed by the properties of the alumina tube at high temperatures. The hot. zone of the furnace was found to be within 10°C. of the highest temperature for yp, close to the 44 found by Nicholson. (1963) for the same type of furnace. However, it •was also observed tn7,t at all temperatures in the range used, the temperature was within 5°C of the highest temperature for about 2.34 along the tube, and within 2°C. for about 1.34. A typical temperature distribution is shown in Fig. 2.3. As the length of the crucible was about J.'', and there were shields at the top and bottom of the crucible, it was taken that •the temperature in the working volume of the crucible was (central temperature) minus 1°C., where the central temperature was-made the highest temperature by suitable position- ing of the crucible, and this gives an error of ::.4°C. due to the hotzone effect alone. • Including the .error due to the mains voltage variation, the total variation in the temperature of the working volume was thus about +_10. 0 C.

2.2. Temperaturejleasurament. Platinum/132', rhodium-platinum thermocouples were used for temperatures up to 1450°C., connected either to a moving- :oil galvanometer calibrated to temperature directly in 10°C, divisions up to 1400°C. , with internal cold-junction compensation, or to a iCambrie' portable 2otent.tol::eter, from which the actual e. 1.f.of the thermocouple was obt,„ine6, and for which the cold-junction correction was then made. For temperatures above 1450°C. platinum--5;,; rhodium / Platinu-:-20% rhodium thermocouples were used both for calibration of the internal tunzsten/265 rhenium-tungsten thermocouple in the "Pyrocore" furnace, and for measurement. I 550-

1540- TEMP.

°C. 15 30-

I 5 20"

1510-

150 0- Temperature Distribution in the Hot Zone of the Pyrocore Furnace.

14 9 0-

148 0-

1 1 3 2 1 0 2 3 BELOW HOT-ZONE CENTRE [INCHES] ABOVE HOT-ZONE CENTRE -. 96 -

At 1800°C. these thermocouples had a comparatively short life, and were used only for short times at this temperature. A regular checking of thermocouples was carried out by comparison at 1000°C. and 1200°C. with two new platinum. / 13:; rhOdium-platinum thermocouples. Fortunately, when platinum -rhodium thermocouples fail they usually do not do so insid- iously; either the ,.ire crystallises and breaks, or the rhodium diffuses into the pure (or purer) metal side of the junction at such a rate that the potential changes substantially in a very short time. The temperature indicated by the thermocouples probably lies within 1-10°C. of the true temperature, and while this error does not affect the consistency of results at one temperature, it is an error which must be accounted for in the comparison of results at different temperatures, as in the plotting of graphs giving activation energies.

2.3. Preparation of Specimens. (a) The Use of Binders. The binders used were beeswax and cetyl alcohol, added in the form of 1, 2, or 3 wt752, solution in carbon tetrachloride.• The binder solution was prepared by dissolving the required weight of beeswax or cetyl alcohol in warm carbon tetrachloride, and filtering twice through Whatman 54 filter paper. If the beeswax solutions are not used immediately, they present some difficulty by crystallisation of the wax, and although this is readily filtered off, the remaining solution is, of course, less - concentrated. 200m1. of the 2 solution were taken, the carbon tetrachloride was evaporated off under an infra-red lamp, and the remaining binder was then slowly heated to 600°C. In neither cas was any residue detectable after being left overnight at 600°C., but a supply of :sir had to be availabe to burn off -9? -

any carbon formed, especially in the case of beeswax. Thus, on gently heating cetyl alcohol in a closed crucible it started to boil, and slowly discoloured to a pale yellow, and finally to pale brown, with a little carbon deposit (1.0- 005 g/g cetyl alcohol) at the end of the evaeoration. The deposit burned entirely away in air at 500-600°C. On subjecting beeswax to the same procedure, there was some discolouration before it started to boil, and this discolouration continued during the evaporation, and the beeswax became dark brown later, with an appreciable amount of carbon deposit ( up to 0.03 g/g beeswax) at the end. The deposit could all be burnt off in air at 600°C.

(b) Pelleting Procedure.

The magnesium oxide powder was taken and to it was added the binder solution. Though 1% and 35 solutions were also used, solutions were found to be most satisfactory. After thorough admixture, the carbon tetrachloride was evaporated off - under an infra-red lamp; the material was stirred during the evaporation. The powder was then transferred to a beaker, and kept in a desiccator over self-indicating silica gel, except when actually being used. A cylindrical steel die, with pressing face 1/2" in diameter, was used to produce the specimens, using pressures up to 50 tons per sq. in. (up to 10 tons total pressure). The compacts were then heated. slowly to 600°C. (over about 24 hours) to burn off the binder, and maintained at that temperature overnight. They were kept in a desiccator over self- indicating silica gel. until required for use.

2.4. Density Measurement.

The two techniques used in density measurement were (a) micrometer screw gauge, (b) mercury displacement hydrometer.

(a) Nicrometgr Screw Gaur,e. The micrometer screw gauge was marked with 0.01 mm. divis-

-98- ions, and distance could be measured to within 0.001 -4- C•0005 mm. However, variation in the length and diameter was considerably greater than this, and the values obtained for the bulk densities have an error of 0.1% theoretical density. The theoretical density of magnesium oxide at ordinary temperatures was calculated to be 3.584 g/cc., using the lattice constant value of 4.212A given by Brown (1963). (b) Mercury Displacement Hydrometer. A scale-pan was supported by a rubber or hollow glass float on a beaker of mercury, and weights were added until the apparatus sank to a certain mark on the supporting wire, as shown in Fig.2.4. --7 The procedure was repeated with a specimen held in the small cage under the float. The copper ark i00 wires of the cage and the scale- Cage pan support were covered with Beaker eicury shellac to prevent amalgam Tort. formation. u = W w , and U = , where u = upthrust due to spec-

Scale-pan imen, W = weight of mercury displaced ---4°P4-0r4rArte w = weight of specimen V = volume of specimen FIG.2.4 Memory Displacement /9= density of mercury. Hydrometer. 1 The rubber float was found to be more satisfactory than the glass float, which showed a tendency to collect a film of dirt on the surface, and to stick to the side of the beaker. The bulk density could be estimated by this method to within i 0.5% theoretical density. In view of the inaccuracy of this method, and the difficulties of preventing amalgam formation and of keeping the apparatus clean, -99-

the micrometer screw gauge was generally used except for cracked and distorted speclmens.

2.5. Polishin. .The specimens were first set in Ceear" resin, full imreg- nation being ensured by repeated evacuation cycles immediately after the resin had been placed over the specimen, to eliminate any trapped air. The initial cutting-down was performed on a wheel with, successively, 180, 240, 320, 4CC and 600-grit self-adhesive silicon carbide baders, using water as a lubricant. Polishing was effected by successively using 14, 6, 3, 1, and 0.4 diamond paste suspended in petroleum jelly, on cellulose fibre discs, with a white-spirit-based lubricating fluid, "Hyprez", supplied by Engis Ltd., who also supplied the other polishing materials.

2.5. Optical HicroscoPy. A Vickers Projection Hicroscope was used with transmitted and reflected light. A "Pointolite" tunsten arc lamp was used for transmitted light, and a carbon arc lamp was used for reflected light. An 811;;:i, objective lens, and a x8 ,.agnification Projecting lens, giving x400 - x9ec El_gnification for 40-90 cm. projection distance, was found to be the most suitable combination in this work. For prloto-micrography Kodak 0-250 ortho 'm.etallographic plates (35,x4) were used, with a light green filter, and exposures of 5-30 seconds for transmitted li,7ht, and 30 seconds to 4 minutes for reflected light. The plate were developed for 3-4 minutes in .Ilford ID-36 developer, or for longer times in Kodak D-?b developer, washed for 30 seconds in fresh l. acetic acid stop- - 100 - bath solution, and then washed with clean water. The plates were fixed for 3 minutes in once-used Ilford IF-2 fixing solution, followed by 8 minutes in fresh fixing solution. The plates were then washed for 30 minutes in running water, and dried. Grain sizes were measured by drawing two mutually perpendicular lines, 5cm. long, on the erojection screen, and counting the number of grain boundaries crossing each of these lines for a number of positions on the Polished surface or outside surface of a specimen, the positions being chosen at random over the surface except where measure:eent of variation of grain size over the surface was required. The measurements were then made at several randomly selected positions in the required area. Fuliman (1953) reported that the average grain diameter is 1.6 times the average random distance between random grain boundary intercepts with a line on a plane surface. If this relation, which is used in this thesis, is incorrect, the results obtained by comparison of grain sizes under different conditions of sintering time and temperature etc., :ueh as activation energies, will not be affected, but comparison of such normal grain growth measurements with direct measurements of sizes of the largest grains (e. g. in discontinuous grain growtn or recrystallisation) would not be quantitatively valid.

2.7. Infra-red S-oectroAotometrv. Infra-red spectrophotometry was carried out using a Perkin- Elmer 237 Grating infra-red spectrophotometer. Sodium chloride discs were used, with the finely-ground sample being, suspended between the discs in a Nujol ,u11. Polystyrene lines at 3.411 and 6.24u were used for calibration.

2.8. Other Techniques, Other techniques used to a lesser extent included electron -101 - midroscopy, electron microbeam probe sl)ectroscopy, X-ray powder diffraction analysis and thermogravimetric analysis; these are described in the relevant part of this thesis. - 102 -

CHAPTER 3. ---••- •

Pure Magnesium Oxide,

3.1. Preparation of Pure Magnesium Oxide 103 (a)Introduction (b)Method (c)Thermal Decomposition of Magnesium Oxalate (d)Efficiency of the Purification Procedure

3.2. Analysis of Magnesium Oxide 122 (a)Methods of Analysis (b)Results

3.3. Hydration Tendencies of Magnesium Oxide 125 (a)Introduction (b)Initial Adsorption of Water Vapour (c)Further Adsorption of Water Vapour (d)Infra-red Cpectrophotometric Studies. - 103-

3.1. PreParation of Pure Manesiu Oxide. (a) Introduction. Oxalates have been used in the detection and analysis of metals, especially calcium (Haslam, 1935). Yaumesium oxalate has been used to determine magnesium, either by aisoiving the it collected precite in acid and titrating against Potassium per,- manganate (Cordon and Caley, 1948), or by igniting to the rxide (Duval and Duval, 1948). Robin (1953), in surcgesting the use of mixed iron and cobalt oxalates in the preparation of the mixed oxides, was among the first proponents of the use of oxalates in the preparation of oxides. Schuele (1959) produced ferro., and ferri-aagnetic oxides from coprecipitated cobalt-iron, nickel-iron and copper-iron oxalates, obtaining very small single-domain crystals. Oxalates have been used in the preparation of catalysts, ferrites, ceritets and "active' metal oxides. :letal oxides from oxalates have been used in sintering studies by Lida and Ozaki (1959), who used nickel oxid from nickel oxalate and other salts, and Brown (1965), who used calcium oxide, magnesium oxide and nickel oxide. Thermal decomposition of oxalates takes place in two stages: Dehydration MC20b.nH,0 n11,0 Decomposition CO CO L 2 In some cases an intermediate carbonate is formed, as found by Padmanabhan et al. (1960) for lanthanum oxalate, and by Freeman and Carroll (1958) for calcium oxalate. The advantages of the use of oxalates in the preparation of oxides are (i) The availability of reasonably pure starting materials of which the cost, though considerable, is not prohibitive. (ii) The possibility of purification of solutions before final it procilAtion by eliminating head fractions of the preciitate by adding the complementary solution or other reagents. - 104 -

(iii)The production of a uniform fine crystalline oxalate which is more easily filterable than hydroxides, and much less likely to adsorb ions from the mother liquor. (iv)The very fine oxide obtained by thermal decomposition of the oxalate, in contrast to that from the nitrate (for magnesium oxide). (v)The lack of anions which may remain after calcination, except for any ions adsorbed on the surface of the oxalate. (vi)'axed oxides may be obtained, where necessary, by coprecip- itation of two or more oxalates, though care must be taken in order to produce the correct relative oroportions of cations. Both normal solubility differences and the formation of super- saturated solutions must be considered. Many of the same attributes may be claimed for basic magnesium carbonate. Hopkins (1959) prepared magnesium oxide by thermal decomposition (l000°C) of basic magnesium carbonate which had been prepared by dissolving pure magnesium metal in it nitric acid and precips.ting with ammonium carbonate. The magnesium nitrate solution was purified to some extent by allowing excess magnesium to stand in the nitrate solution, which precipitated some impurity metals as their insoluble hydroxides. Spectrograrhic analysis of the magnesium oxide indicated a purity of better than 99.88%. Leipold and Nielsen (1966) used excess nitric acid in the preparation of their magnesium nitrate solution, and then neutralised with ammonium hydroxide solution. The method of purification was to bring the magnesium nitrate solution into contact with three consecutive washes of a chelat- a7ent (0.5 molar thenoyl-trifluoracetone (TTA) in 4-methyl- 2-pentanone), starting Ath twice-used TTA solution, and finish- ing with fresh solution. To this purified solution of magnesium nitrate was added excess aqueous ammonium carbonate Solution, which had not been purified, and the resulting precipitate was - 105 -

filtered off and washed, then calcined in vacuo at 650°C. Spectrographic and flame photometric analysis revealed metallic impurities of the order of 400 ppm, and possibly as much as 0.12% of fluoride, derived, presumably, from the TTA. However, it was considered that the oxalate probably gave an opportunity for a more efficient, simpler purification procedure, and the efficiency of purification is discussed later. Classen (1879) reported the precipitation of magnesium oxalate by addition of potassium or ammonium oxalate to solutions of magnesium salts, proposing it as a method of analysis, even though there was consistent loss of several percent of magnesium in his experiments, Other alkali metal oxalates and oxalic acid have since been used as precipitants. Peisach and Brescia (1954) studied the crystallisation of magnesium oxalate from solution, and concluded that the ions associate rapidly to form Mg0204, and form a critical nucleus of two molecules, also rapidly; the rate-determining step in the crystallisation is the addition of a third molecule to form a nucleus which grows into a crystal. The crystals are clear and rhombic under the microscope, and appear white in aggregate. Scholder (1927) described magnesium oxalate, which crystallises in the form of the dihydrate, as an auto-complex, with a solubility of 300 mg/i. at 18°C, Other reports of the solubility give figures as high as 700 mg/l. at 16°C. and 800mg/i. at 100°0. However, the solubility of magnesium oxalate is notably higher in aqueous solutions of alkali metal and ammonium oxalates; the solubility is 300 times the normal value in the cace of; solutions containing alkali metal ions. Magnesium oxalate is virtually insoluble in organic solvents. The crystals have M.N. 143.37 and density 2.45 ace. The temperatures of dehydration and thermal decomposition of magnesium oxalate depend to some extent on the conditions under -106--

which the experiment is carried out. The rate of heating of the sample alters the apparent decomposition te:Terature. The re- Portec: dehydration and decomposition temperatures of magnesium oxalate are given in Table 3.1.

Table3„1.ThermaLDecompesitionpfMarmesium Oxalate Dihydrate. Rerdorted by: T dehyuration Tdecomposition !Duval & Duval (1943) 176-233°C. 377-430°C. Kawaj.:aki (1951) 125-220°C. 400-500°C. :Robin (1933) 175°C. 385°C. lUgai (1954) 196-212°C. 421--419°C. (suer..,,) iErdey & Pauli!: (1955) 145-230°C. 340-430°C. " 1 Brown (1963) 145-260°C. 395-530°C.

In the preparation of pure metal oxides, the main requirement is purity rather than yield, and thus the opti;lisation of the yield with respect to the magnesium ions in solution, which has occupied many investigators in the past, is not of concern in this case. It is desirable to restrict reagents to those which will, it if associated with the orecir4te of . 1agnesium oxalate, give only magnesium oxide after calcination, and thus alkali metal oxalates were not used as precipitants, and only manesium nitrate was used as the other reagent. In view of the high calcium content found by .Frown (1963) in magnesiu::., oxide obtained by calcining magnesium exalte procinitatrA by oxalic acid, a=onium oxalate was used in the preparation, which consisted simply of admixture of hot purified solutions of ammonium oxalate and magnesium nitrate.

b) Method . The reagents used in the preparation were all "Ar,-:laR" analytical grade reagents (Hopkin & Ltd.), except for the 1.1a3ncsiu:.:,- which was redistilled magnesium supplied by - 107 -

Ma:;nesium .1ektron Ltd., with a purity better than 99.97. Manu- facturer4s batch analyses of two batches are given in Table 3.2.

Table 3.2. Manufacturer's Batch Analyses of Redistilled MaE7:2esium. ::dement Impurity content (cation) - I-- Fe 0.001 0.001 t:0.001 0.004 t'in 0.001 0.004 Zn <0.01 0.001 Al <0.007 0.005 Si 0.002 C.005 Na n.d. 0.001 Ca 0.002 0.001 Pb <0.001 0.001 Cu

Nitric acid was used. to dissolve the magnesiu::,, because any magnesium nitrate associated with the magnesium oxalate will de- compose on heating;'. Hydrochloric acid introduces chloride ions which are difficult to remove by washing; it was found by Hopkins (1953) that the maRnesium oxide obtained by calcinfnr.,;. magnesium carbonae precipitated. from magnesium chloride solution contained a considerable amount of chloride, and a si. j.lar result was obtained by Livey et al. (1957) for magnesium oxide obtained by calcining magnesium hydroxide precipitated from magnesium!. chloride solution. A typical preparation is outlined below. Cut blocks of metallic magnesiu were thoroughly washed in 211 nitric acid--10 Teepol solution to clean off any grease or dirt as well as the surface layer of magnesium. The blocks wore then washed in 2N nitric acid followed by two changes of distilled water. They were then mopped dry with clean filter-paper, weighed, placed in a large beaker (5 1.), and covered with distilled water. Concentrated nitric acid was then added to produce a vigorous - 108-

reaction, controlled when necessary by cold water in a vessel surr- ounding the beaker, or the addition of a little cold distilled water to the reaction. The reaction was maintained by frequent additions of small aliquots of nitric acid until a total of 1915 ml. had been added, leaving a few small pieces of magnesium metal unreacted. The solution was then boiled to reduce the acidity by further reaction, and allowed to stand overnight or over a week.- end. A -,Drecioitate of magnesium hydroxide then formed, and the magnesiuM retal was tarnished by the deposition on its surface of metals lower in the electrochemical series. The precipitate and unreacted magnesium were filtered off on a 'Jhatman No.54 paper at the pump, the magnesium ,/L.s separated off, and the magnesium hydroxide precipitate was washed and dried. From the weights of magnesium and magnesium hydroxide it was calculated that 282 g. of magnesium had dissolved. A further purification of the magnesium nitrate solution was effected by addition of 50 ml. of 507 ammonia solution, with stirring, and the hydroxide precipitate was allowed to settle overnight, .filtered off, dried: and weighed, giving 20.5 g. magnesium hydroxide, and leaving 270 g. magnesium equivalent in solution. The filtrate was then taken, and to it was added 500 ml. of the ammonium oxalate solution (see below); the suspension was boiled for a few minutes, and left to settle overnight. The magnesium oxalate precipitate was then filtered off on a 'lhatman No.54 paper at the pump, and washed with a little water, and the filtrate was removed. The precipitate was further washed with water and acetone, and dried at 100°C. The first head fraction of magnesium oxalate weighed 35 g. A second head fraction was obtained by treatment of the filtrate, and weighed 25 g. The volume of the filtrate was then 4 1. Ammoniva oxalate (1578 g.) was dissolved in distilled water (8 1., two lots of 4 1.), and the first head fraction was obtained - 109

by progressively adding magnesium nitrate to each of the boiling solutions, until vigorous stirring produced a precipitate. little more magnesium nitrate solution was added, and after leaving overnight the.precipitate was filtered off at the pump.,,. and washed with distilled.water, and the filtrate was removed:.The watarandwith precipitate (40 g.) was washed with more/acetone, and dried at 100°C. The procedure was repeated for the. second Read fraction (20 g.). The purified solutions of magnesium nitrate and ammonium oxalate were admixed hot, with stirring, and left to settle overnight. The fine crystalline precipitate of magnesium oxalate..'was• filtered off at the pump, thoroughly washed with distilled water, and then with acetone, and dried at 100'C. Yield 1080. g. (66%). Most (1037 g.) of the oxalate was used to produce magnesium oxide by calcining at 800°C. The calcining schedule consisted of placing 100-150 g. of magnesium oxalate in an 800 ml. platinum beaker, the top of which was covered by. a platinum evaporating dish, and placing this in a cold silica pot furnace, the temp-,.. erasure of which was raised over a period of about six hours to:.. 800°C. The furnace was maintained at 800'C. for 10 hours, and • then turned off. Attempts at placing he beaker in a warm furnace (150-300°C,) resulted in -aaterial being sprayed out of the beaker into the furnace. The yield (SPecimen 41010) was 255 g. of magnesium oxide (61%, allowing for the magnesium oxalate not decomposed.) Oxalic acid and ammonia solution were used to produce ammonium oxalate solution in later prebaratiOns, because this.is less expensive than the corresponding quantity of solid ammonium oxalate. The magnesium oxalate Precipitate consisted of ..a. loose agglomerate (Plato 3,1(a)) of small magnesium oxalate crystals (Plate 3.1(b)), 5-1511 in diameter. •

•

Plate 3.1(a) x600 Plate 3.1(b) x600 Magnesium; oxalate dihydrate- Magnesium oxalate dihydrate loose agglomerate. crystals.

Plate 3.2. x600 Thermal decomposition product of magnesium oxalate dihydrate. 'aopliod zrpTxo TnTsouZPr; zo qdraScaoToqouLd uoa400Ta 'C'c aVaId

- , - 000 'oot y

- ITT - - 112 -

On:thermal decomposition the crystals retained their overall shape, as shown in Plate 3.2., and the final product consisted of a large number of cubic magnesium oxide crystals, with an average side length of about 200 A, as shown in Plate 3.3. (c) Thermal Decomposition of Magnesium Oxalate Dihydrate.

Duval (1953), Freeman and Carroll (1958) and Brown (1963) reported the formation of stable carbonates in the thermogravimetric analysis of calcium, strontium, and barium oxalates, and the temperature range of stability increased with increasing atomic weight. Magnesium oxalate has been reported as being decomposed directly to the oxide, with no intermediate carbonate stage. How- ever, the monotonic variation in the stabilities of the carbonates produced in the thermal decomposition of the oxalates is modified by the changes in the crystal structure of the carbonates. Barium carbonate, strontium carbonate, and the low-temperature form of calcium carbonate, aragonite, are orthorhombic, with 4-coordination and monotonically decreasing lattice parameters. The form of calcium carbonate stable above 400°C., calcite, and magnesium carbonate are both .trigonal. Both calcite and magnesite have distorted face-centred rhombohedral structures. The range of stability of calcium carbonate is given as 420,-660°C., and thus it may be assumed that calcite is the form present. Table 3.3 gives relevant data in decreasing order of stability.

Table 3.3. Decomposition Temperatures of Carbonates in Thermal Decomposition of Oxalates. Structure : Temperature Range (°C.) BaCO i orthorhombic >476°C. 3 I .SrC0 .5- I orthorhombic j 520-1100°C. CaCO3 trigonal 420-660°C.

MgCO3 trigonal not stable (?) - 113 -

In a plot of weight versus temperature, two regions of weight loss have been observed in the thermogravimetric analysis of magnesium oxalate, corresponding to dehydration and decomposition, while the decomposition of calcium and strontium oxalates is shown WLthi4D stable carhonate beta, aa UB in two stages,/and the barium carbonate :termed in-the first stage of decomposition of barium oxalate is stable up to the limit of the thermogravimetric analysis apparatus used. In the present work, a sample of 1 g. of magnesium oxalate dihydrate was heated to 1000°C, at the rate of 10°C. per minute on a Stanton TR/01 thermobalance. A plot of total weight versus temperature is shown in Fig. 3.1. The range of dehydration is 190-350°C., and that of decomposition 420-590°C. Slower heating would weight the ranges into the lower part of their respective scales. A distinct change in the rate of increase of temperature was noted at about 530°C. , corresponding to the weight loss appropriate to the formation of magnesium carbonate, and this change indicated that the decomposition reaction became effectively more exothermic than before. This more exothermic nature of the reaction continued until the weight loss corresponded to the formation of magnesium oxide. This may well indicate that the decomposition of magnesium oxalate does not proceed directly to magnesium oxide, but via an intermediate carbonate: Mg(00C) 2 03 .eCO MgCO3 e. CO2 . The magnesium carbonate so formed would appear to be much more easily decomposed than calcium carbonate formed under similar conditions, tending to make the two stages appear as one. As the temperature of decomposition of magnesite has been previously given as about 350°C., it would be useful to obtain more information on the process of decomposition by examination of the effluent gases to see if there is preferential evolution of carbon monoxide during the early part of the decomposition. As it was only relevant to check the course of dehydration and decomposition in this study, a more thorough investigation of the phenomenon was not carried out. °I0 wt. •

.mm01. 41mm .•••••. — — —14000i 21-1 20 M.W. 148'37

149(004i H z.0 M . W. 130.56

— — — — _143(0001 . M .W. 112.34 70

—11 /441C 03 PA M. 114.33

Fig. 3.1 30 The rmograyi metric Analysis of M90 M.W. 4042 Magnesium Oxalate Dihydrate.

0 100 200 300 400 500 6 00 700 800 TEMPERATURE C°C]

(d) Efficiency of the Purification Procedure in the Elimination of Impurities. The total concentration of imourity elements expected from the starting materials may be calculated by using the batch analyses of the high purity magnesium supplied by Magnesium Elektron Ltd., listed in Table 3.2, together with the given maximum limits of impurities in AnalaR chemicals supplied by iopkin and Jilliams Ltd. These are tabulated as impurity concentration in the working solutions in Table 3.4 and Table 3.5.

Tak1e.. 3.40_TheContentof Impurity Elementst and_their Concentration in Magnesium Nitrate•...._•._• Solutions. __..______, •,_• ;Contribution from Contribution fromfTotal concentration lement131 - 00 g. hg, in gs. 2 1. HNO3, in ,i,mslin gms:1, (4 1. soh) Na , n.d. 0.003 none 1 0.0003 Ca 1 0.006 0.003 - C.0015 i 0.0008 Al I 0.02 0.015 - 0.005 0.004 Si i 0.006 0.015 - 0.0015 0-004 hn ! 0.003 0.012 - 0.003 Fe ; 0 -003 0.003 0-002 1 t= 0.0013 Ni i 0.003 0.012 - ' 0.0008 0.003 Cu ; 0.003 0.003 - 1 0.0008 0.0008 Zn i 0.03 0.003 - 0-0075 0-0008 Pb ! 0-003 0.003 0.004 0.0018 0.0018 As i _ - 0.00004 0.00001 0.00001

Table 3.5. The Content of Impurity Elements and their Concentration in Amoniup Oxalate Solutions, ContributionConc.in Contribution from !Conc. in 1 ., Element from onmadum, g/l. oxalic acid ,ammonia Sum , g/l. oxalate 16CCV (8 1.) 1440g i 1100g. (8 1.) in gms in gras. ;in cms.lin gins.i No ... , - - - - Ca 0.008 1 0.001 0.029 - 0.029 ! 0.0036 Al - 1 - - - Si - - - 0.011 0.011 0.0014 Mn - - 1 - Fe 0.003 10.001 0.0072 0.0002 0.0074 0.0009 Ni - , - ' - Cu - 1 - - 0.0001 0-0001! 0.00001 Zn - - - - - ! - Pb 0.008 10.001 0.0072 0.0004 0.00761 0.00095 I - _ - 116-

The information available on the solubilities of the hydrox. ides and oxalates of the impurity elements is limited on the whole to simpler systems. However, so7ile relevant data are available. Consideration will first be given to the solubilities of hydroxides in 2.8-4 M. magnesium nitrate solution (the range of concentrations used in the preparation). The information is restricted almost entirely to the solubilities of the hydroxides. After the hydroxide precipitate is left to coe to equilibrium, the pH of the solution is not more than 10, and thus the formation of complex anions by ayiDhotericoxides, such as zinc oxide, can be ruled out in this case. A reduction of pH from 13.5 to 13 reduces the concentration of zinc ions (Seidell, 1940) from 0.3$ to 0.036 g/1., and thus it is unlikely that there will be a significant contribution by complexin at pH 10, as the highest reported solubilities in neutral water are about 0.008 g/l. Table 3.6 gives the solubility of the hydroxides of impurity elements in water, given as the weight of metal per litre, together with relevant comments, and the total possible weight of the imp- urityetal remaining in 4 1. of magnesium nitrate solution after two precipitations of the hydroxides, assuming no interactions giving rise to greater solubilities. In the literature there is a great deal of inconsistency of results, and the highest figure has been given where the disagreement is by less than a factor of two, otherwise the ranges of reported values are given, and the highest value use.d in the computation of the maxium weight of element present in 4 1. of solution. - 11? —

Table 3.6. Assessment of Maximum qeight of ImPurities in 4 1. of Mar,resium Nitrate Solution. Temp. Kement 0- Comments wt. in 4 1. g.meta1/1. off(No ) soln. 3 Na v. so1. Ca 1.0 0-100 _ ... .3.-D _ Al 0.00036 18-30 reduces Al conc. 0.0014 (stops)* - 1.-W-3...... _—__. _ O075- - 2 (•20 25-9 0 Dissolved as 310 0-30 at 25°C. 0• 0012 18 -0048 stgag _ __0_•_Na3.D._.LatO.P_)__.. !0.00046-: Fe 0-0168 0.o042 rm.T . Fe(OH),- (stops) Fe ' 1.53x1° rm T Fe(CH) 0-0146 0-00366 Co 0-0017 20 (stos) Ni - 6d8 0 032 "2 071.7 1.97.1p - • rm.T. Most values given°. 0-039 Zr. f, -- 008 ox10 -) Pb . 0-52 *(stops) indicates that the hydroxide controls the purification, with respect to that element, in the process.

The same treatment may be carried out in the case of the oxalates of the impurity metals, but it must not be forgotten that the two different systems must be considered. 7.1hile the magnesium nitrate is unlikely to affect the solubilities of me, oxalates vary greatly, ammoniu oxalate is known to form solule comple7es with some elements which would otherwise preciitate as insolusle oxalates. The known data are summarised in Table 3.7.

- 118 -

Table ").7. Assessment of Ma:dnun -Arei:.:ht of IL:purities retaining in -Vorkino- Solutions.

Solv T Tiotal weight remaining in Element ' oc. !Comments 3°1Y'in water • B-4 • ON 141. MOO ) 81.(NE B ) (00C). 1 3 Z, . • g/3.. xalate 'solution - H 0 solution 1 ,ii I gms. 2 gas. - 12 1 9, Ca 0.002 rm.T.S=1.78x2.0 •lxi0_8 0.008 2x10- -'7-, 0.004 95 -rr «or r .5x10 -1.4x10' Al oxalate I- Si _ no oxalate 0.06 0 anhydroul- in 0.08 20 (oxalate v.sol 0.52 >?100 0.11 35 _TOxlesssl. 0.01 4- 20 Fe 0.069 Fe2+ 0.07? 0.28 0.55 0.081 100 I 5+ Fe v. insol Fe v. little v. little** Co 0.0085 18 0.0135 25 0.054 0.108 Cu 0.01 25 insol. in . 0.04 v. little __.. __ .._ .______..___gonc. oxalateI Ni [9 • 0012 13 0.0048 0.0096 _ _ 0.00P4- Zn 0.0070 rm. T. lv.so1. -. 0.028 large wt. Pb 0.0011 18 0.0044 0.008 ** In vie,:! of the conditions in the preparation, ferric ions are expected in solution. _ .

. Manganese and zinc form soluble complexes in oxalate solutions which are increasingly soluble at increasini,; oxalate concentrations. Co0-2er forms solutions in which the concentration of copper reaches a maximum value, and then decreases again, on increasing the oxalate concentration. Table 3.8 gives the reported variation in solubility with concentration of oxalate. While it may be seen from Table 3.7 and Table 3.8 (overleaf) that the solubility of manganese oxalate in -water is quite high, and that in oxalate solutions is even higher, virtually all the anganese in the original . magnesium will hays been precipitated - 119 - as the hydroxide.

Table 8. Solubility of marys'anese 7inc andcoDoer ions in oxalate solutions (in g.-mo1.7-1.). Ammonium _2+ Ammonium zn2,; Sodium ; m Cu oxalate oxalate oxalate o•ooJ - -0.53FA 6.05 - o•Oo22 -x 0.025 0.479,d 0.10 0.0055 0.01 i 0.0049 0.050 0.761 0.15 0.0106 0.02 1 0.009j 04125 0.20 0.0174 0.04 0•0171 0.245 3.9701! 0.25 0.0254 0.06 0.0247 0.245 4.005 0.08 0.231 4.650 i! 0.092 ' 0.0230 0.167 0.0119 0.2_32 0.0030 0.24 0.000

Any manganese in the ammonium oxalate will remain in solution, and may become associated with the final precipitate of magnesium oxalate. However, up to 0.032 g. of zinc will have remained in the magnesium nitrate solution after hydroxide precipitation, and virtually all of this will remain in solution when the ammonium oxalate head fractions are introduced. At the same time any zinc in the ammonium oxalate will remain as a soluble complex. Thus there arises the possibility that if there is quite a large concentration of zinc in the ammonium oxalate solution, it will be preferentially precipitated when the oxalate concentration in the solution is reduced on precipitation of magnesium oxalate. Only 0.026 3. of zinc, a figure of the order of the-quantity of zinc expected in the ammonium oxalate, would give an impurity concentration of 0•01jb in the magnesium oxide if it were all precilAtated. On the basis of the. lower figure given for the solubility of zinc oxalate in water, it is epected that the weight of zinc in 12 1. would be of the order of 0.026 g., and thus there is so:Ae possibility of precipitation of zinc. Comparison of Tables 3. 5, 3. , and 3.8 shows that the method - 120 - may be expected to be extremely efficient in the removal of iron (less iron is expected to remainY.Llution than would give 1 part per million (ppm) if it were all coprecipitated with the magnesium oxalate), and aluminium (6 ppm). The process should restrict the concentration of manganese, nickel and lead derived fro:::1. the magnesium nitrate solution to 20 ppm each, and that of chlcium to 32 There should be no calcium derived from the oxalate solution in the final prOduct, and thQ nickel and lead should be restricted to a quantity corresponding to 40nand 36 ppm, respectively, from the oxalate source. The process is less effective for the other elements, only restricting copper and zinc from the nitrate solution to 70 and 110 ppm. respectively, and not reducing the concentration of alkali metals or silica at all. The hydroxide head fraction should be most efficient at removing aluminium, manganese and cobalt present, and most iron, nickel and zinc. Some silica is likely to co-precipitate with the other hydroxides. Thus Brown (1963), in analysis of a similar hydroxide precipitate, found Fin 0.20, Si 0-10, Fe 0.06, Al 0.02, Ni 0.02, and some Cu and Ca. The oxalate head fractions should eliminate nearly all nickel and iron frb::‘ the magnesium nitrate solution, and much of the calcium. The oxalate head fractions from the ammonium oxalate solution should be very effective in the removal of calcium from solution, and iron should be excluded and any nickel and lead reduced in concentration. As explained above, only zinc is expected to be preferentially co-precipitated with the magnesium oxalate en the basis of solubilities alone, but there is the possibility that considerable quantities of alkali metals and silica, some calcium, nickel,copper and.lead and a little aluminium from the magnesium nitrate solution, and some lead and the silica from the ammonium oxalate solution, - 121 -

will have reached the final precipitation. It would appear that the elements most likely to appear at contents greater than 10 ppm. in the final product are: Calcium from the original magnesium. Although there should be less calcium than would normally allow the solubility product to be exceeded, unless there is a considerable excess of oxalate, it is likely that much of the remaining calcium (equivalent to 32 119.) will be associated with the magnesium oxalate. Zinc from either source. Preferential precipitation of virtually all zinc in solution. Silicon (as silica) is unpredictable in its behaviour. The process will not have eliminated much of the silica, and it- is likely that some silica will be associated with the final product. These predictions are made on the basis of the stated impurities. in the starting products, and the effect of any increase in the concentration of an element may be assessed from Tables 3.6 and 3.7. It is also possible that the glass apparatus, though it was scrupulously cleaned, may have contributed some sodium, potassium and silicon. -122-

3.2. The Analysis of Nagnesium Oxide. (a)_Methods of_Amplysis. Spectrographic analysis of magnesium oxide prepared from magnesium oxalate was carried out by Brown (1963), who detected only calcium (1 ppm.) in the product. Unfortunately, though this method is sensitive for the detection of calcium and copper in magnesium oxide (claimed limit of detection : 1 Pp.), and fairly sensitive for nickel (9 ppm.), it is much less successful in the detection of silicon (30 ppm.), manganese (40 ppm.) and aluminium (100 ppm.), Flame photometry was used by Brown to analyse for sodium, and this method is probably the most sensitive available for the detection of alkali metals in magnesium oxide. In view of these difficulties, it was decided by Duff (1966) to analyse for impurities by conventional spectrophotometric, flame photometric, and atomic absor:tion spectroscopic methods. The impurity elements were analysed for as follows: Sodium and potassium: Flame photometry with appropriate filters. Calcium: Atomic absorption spectroscopy. Aluminium: Spectrophotometric examination at 530 of a solution viith .•:-.olochrome cyanine RE at pH 5.8 (early determinations at pH 4.5 appeared to give lower results), Fe and Cu' being masked with potassium cyanide. The iron was reduced to Fe with ascorbic acid. Silicon: Treat,.ent with ammonium molybdate g,ve silicomolybda,e, which was examined spectrorhotometrically at pH 1.5 and 430 Manganese: Oxidation with potassium persulohate gave permanganate, which was examined at 5a5 sp. - 127

Iron: Reduction by ascorbic acid to Fe++, followed by reaction with 0 1:10-phenanth46ine and measurement at pH 3.25, 510 IT. Cu and Ni+÷ masted with E.D.T.A. Nickel: The dimethylglyoxime product was extracted into chloroform, and with Cu++ masked with sodiun thiosulbhate, Fe — maskRC with sodium tartrate, and Mn masked with ammoniva: citrate, measurement was made at 365 mu. Copper: The 2:9-dimethy1-1:10-phenanthrolino comolex vas measured at pH VDO mu, interfering ions being; masked with sodium citrate. Zinc: The dithizone complex in 50 methylcellosolve (ethylene glycol mono-methyl ether) at pH 5.5, with a buffer comblexing solution of sodium thiosulphate, sodium acetate, potassium cyanide and acetic acid, Fe and Mn being conplexed with 25% citric acid, was measured spectrophotometrically at 525 mp. Lead: Measurement at 3'71 mp as the hexachloroplumbate in 1:1 acueous hydrochloric acid.

(h) Results. The results of the analysis at first appeared to indicate that the only element present in a concentration of more than 10 ppm. was silicon, with a concentration of -20 ppm. when ammonium oxalate was used in the preparation, and "'50 ppm. when ammonia and oxalic acid were used. However, re-examination of the data some tine later revealed a series of errors, and the corrected results gave increased impurity levels by a factor often for nearly all elements analysed for. In the revised data there is little difference between the silicon 1:o2urity levels for the magnesium oxide -124- prepare,a using the two oxalate starting materials. In view of the birth silicon • content, thought to be introduced by dissolution of silica in the ammonia solution on storage after manufacture, Duff prepared ammonia solution by isothermal distill- ation into water in a polypropylene beaker. This was effected by placing glass beakers full of 0.380 ammonia solution and the polypropylene beaker of water in a. large sealed container, and leaving for several days. The preparation of magnesium oxalate was carried out entirely in polypropylene apparatus. • The analysis of this material. may be seen in Table 3.9., together with those of samples of magnesium oxide prepared for the sintering studies in this thesis, and a sample prepared by Brown(1963).

Table 3.9. Analysis of_ Ma.gnesium Oxide Samples for Impyites..._. Iiffy Conoentration in pours for Element 41020 1 41103 a Duff (1) Duff (2) Brown Na 23 22 21 30 25 30 K 17 16 16 20 15 ,aCa ? ? 20 60 20 30 Al 14 17 16 44 48 50 Si 89 89 93 220 80 80 Mn (1. <1 <1 <1 2 Fe <10 <10 <10 10 10 20 Ni <1 <1 <1 2 2 2 Cu 410 <10 <10 10 11 10 Zn <10 1 <10 <10 10 <10 20 Pb I 2 <1 <1_ 1 Total (17 Ca? 178 <199 408 224 245 E? a: Mixed batch used in sintering studies Duff (1): Prepared using glass apparatus Duff (2): Prepared using polypropylene apparatus.

The first two batches of oxide prepared contained more sodium and potassium than later batches (e.g. 41010: Na 65 ppm, K 38 yom), while the concentration of other elements was the same. This was presumably due to Na and K r being dissolved from the surface of new apparatus, despite every precaution being taken to ensure cleanliness of apparatus. -125-

3.3, -ridration Tendencies of Marmesium Oxide. (a) Introduction. In the present study it was required to know the characteristics of hydration of magnesium oxide, as handling in desiccated conditions during all the operations of addition of binder and pressing present some difficulties, and it was thus preferable for the material to be handled in the open atmosphere. Anderson and Morgan (1964) report that water-vapour, even at pressures as low as 5 mm. Hg, enhances agglomeration and growth of magnesia by a factor of 103 by a surface diffusion process. In view of the fact - that the sintering studies and the initial calcination were carried out in atmospheres with a much higher water vapour pressure than this, a factor of greater significance in the present work is the possibility of surface modification during the heating up to sintering temperatures, due to dehydration of hydrated magnesium oxide . Hopkins (1959) studied the rate of uptake of liquid water by magnesium oxide prepared by thermal decomposition of magnesium carbonate, and found that the amount of water corresponding to the formation of the hydroxide, Mg(OH) was taken up within 2 2' days, though the actual rate of uptake varied between specimens. With regard to the rate of hydration due to atmospheric water vapour, however, Moran (1963) reported that magnesium oxide, obtained by calcininj the basic carbonate, left in the atmosphere for over a year gained in weight only about the quantity of water expected for adsorption on the surface of the magnesia of a monomolecular layer of hydroxyl ions. Using the value of 15 A- for the area covered by a molecule of chemisorbed water, given by 2 Gregg (1957), i.e. 0.067 molecules/ A , the figure derived for the particle size is just over half that observed in electron micrographs. The work of Webster, Jones and Anderson -(1965) and Anderson - 126—

and Ho lock (1962) indicates that the theoretical maximun limit for a - ovolayer of chemisorbed water corresponds to a coverage of 0.11 2 molecules/ A- ( 9 e/molecule), but any adsorption above 0.08 molecules/ A2 (12.5 A2/molecule) gives rise to narrow lines in the N.M.R. spectrum indicating the presence of physisorbed water. The value of 12.5 A2 per molecule is used in this thesis to indicate one comr'1ete chemisorbed water layer. The crystallite size of the magnesium oxide powder was measured by taking two sets of 50 random Crystallites on the electron micrograph shown in Plate 3.3, and measuring their side lengths. The two sets show sizes within 10% of each other. The average size of the crystallites was 210 A ;:a 5%, and the root mean square (RMS) valUe was 220 A + 5%. It must be emphasized that these values are taken from only one photograph, taken at the edge of a magnesium oxide- "pseudocrystal", and the true average and RMS values may vary somewhat from this figure. However, this gives the order of magnitude of the size of the oryst:Lllites, and thus the value of 0.044 molecules/ A- per 1% adsorption of water, derived from the RMS value of 220 A, is used. The magnesium oxide was handled in air for as short .a time as possible. =nevertheless, it was allowed to cool down in the furnace, which was open to the atmosphere, it had to be transferred from the :-;latinu beaker in which it was fired to a glass jar for storage, and the storage jar was opened from time to time for use, and thus the magnesium oxide did adsorb some moisture, — 127 -

(b) Initial Adsorption of Water Vapour. :Samples of magnesium oxide from various batches were fired for 1 hour at 1200°C., and were usually found to contain about 0.85 2 wt- water (0.0374 molecules / A ). corresponding to 52.7% coverage of the surface of the magnesium oxide. However, the water con- 2 tents varied, being as low as 0.23% water (0.0101 molecules/ A , 12.6/0 coverage) in one case, and as high as 1.04% water (0.0457 molecules/ A2, 64.4% coverage) in another. The magnesium oxide used in the sintering experimehts, consisting of several batches mixed thoroughly together, slowly adsorbed more moisture owing to the jar being opened from time to time to take out magnesia for use. .2 After one year 1.35 of water (0.0526 mol ecules/ R 74';'; coverage) ha been adsorbed, and after two years 1.78 of water (0.078 mol- 2 ecules/ A , 98% coverage) had been adsorbed. Magnesium oxide containing 1.73% of water was taken and placed in dishes to a depth of - 3-5 mm.. The rate of adsorption of water was studied by measurement of the increase in weight in the atmosphere after various intervals of time, with intermittent stirring. The temperature of the ateosphere was 24°C., and the relative humidity, as determined by a paper hygrometer, wee 50 5%. The adsorption of water is fairly fast at first, but the rate falls off quite rapidly with time, and after the total.water content has risen to about 45, ar about two lay3rs coverage, the rate falls to a small value. The initial adsorption is shown in Fig. 3.2. The same magnesium oxide mixed batch was taken, and a sample was heated at for 1 hour, and the rate of hydration was also determined. Initially, the rate of hydration of the calcined material was high, giving an increase in weight of 2 mg/min. for a 3 g. sample while in the platinum crucible used for firing, which still had its lid on. This represents an increase in the coverage of the surface of nearly per minute in the almost closed container. The dry weight of the oxide was obtained by extrapolating st• eits

WATER HYDRATION OF MgO

SORPTION

3- R E HYDRATION OF DEHYDRATED MgO

Fig. 3.2.

initial Adsorption of Water Vapour.

2 4 6 8 10 TIME 111OURS1 - 129 - the weight back to the time when the oxide had cooled to about 150-200°C. The correction so obtained was small (about 2 mg.). The rate of rehydration of the dehydrated sample is shown in Fig. 3.2., in a graph of weight of water sorbed versus time. A plot of weight of water sorbed versus the square root of time is shown in Fig. 3.3. The rehydration of the dehydrated magnesium oxide follows a straight line up to about 2 wt-% water adsorbed on this graph, followed by a decrease in rate, whereas the as-stored material shows a curve of continuously decreasing rate, though the initial adsorption of this material, VD to a total water content of just over 2%, is approximately a straight line on this plot. The linearity of the graph of rehydration of dehydrated magnesium oxide with the square root of time is confirmed in a plot of logarithm of weight adsorbed (w) versus logarithm of time (t), which has a slope of 0.50 i 1%. This is in agreement with 0.5 w=kt , as this gives log w = log k 0.5 log t, where k.::constant. Haywood and Trapnell (1964) point out that a square-root time dependence for chemisorption corresponds to a diffusion-controlled process. These results indicate that the attachment to the surface during the adsorption of the first 2 wt-55 of water is controlled by the diffusion of the water to the surface on which it is being adsorbed, and that after this initial stage the ante of adsorption is controlled by the properties of the surface. The'slight difference between the slopes for the two samples is due to small diff- arencas in the conditions for diffusion of water to the surface, and does not affect the significance of the linearity of the plots. The figure of 2 wt-% of water indicates either a monolayer on the surface of cubic particles with a RMS value of 200 A for the cube edge, or 1.10 layers on the surface of cubic particles of HYDRATION OF MgO 4- wt.% WATER SORPTION

RENY DRATION OF DEHYDRATED M90

Fia. 3.3.

Initial Adsorption of Water Vapour vs. Square Root of Time.

216

vrTINW [MINUTE% L -131 -

edge 220 A (RFS value). In view of the uncertainty of the exact average size of the particles, this is a good correlation with the adsorption of a monolayer on the surface. Thus it appears that chemisorption of water occurs, under normal atmospheric conditions, to form a complete monolayer. It• is believed that sorption occurs by formation of pairs of hydroxyl .groups from water aolecules and the oxygen ions in the crystal surface, where they are preferentially sited on account of their much greater polarizability. It alSo appears .that the rate of this sorption is controlled only by the rate at which water vapour can approach the surface.

(c) Further Adsorption of Water Vapour. Adsorption studies were made at room te,Iperature (24-26°C.) in the atmosphere, which had a relative humidity of 50,) (determined by a paper hygrometer, error 5% r.h.), and contained some carbon dioxide, which nay have led to the formation of some basic magnesium carbonate, at the time of the experiment. Studies were also made in controlled atmospheres, which were obtained by placing saturated soluti:ns- of calciuLl chloride or barium chloride over their respective solids at the bottom of a desiccator, giving relative humidities of about 30% and 83% respectively. A pure water ateosphere was also used. If only adsorption is occurring, that is, if the only interaction of water vapour with the surface of the magnesium oxide is the building up of layers of water on the surface, then, at constant vapour pressure of water, equilibrium should be reached where the rate of sticking of molecules to the surface is equal to the rate of spontaneous evaporation of the adsorbed molecules to the environmental atmosphere. On increasing the water vapour pressure, thermodynamic considerations will dictate that a part of the additional water in the system shall be adsorbed on the surface, -132- and conversely water will be desorbed if the vapour pressure is decreased. The actual additional quantity of water adsorbed, or the quantity desorbed, on changing the vapour pressure will depend on the magnitude of the pressure change and the nature of the material concerned. In addition to the reversible physical adsorption of water, many surfaces, including those of refractory oxides, will adsorb water to form an array of chemically-bonded hydroxyl ions. Further, reaction may occur in which the physically adsorbed water becomes more strongly attached, and a reaction front may proceed through the crystal. The adsorption of water vapour by magnesium oxide under atmospheric conditions did not stop at a single chemisorbed monolayer of water, as can be seen from Fig.3.2. Though the rate of adsorption decreased, water continued to be adsorbed, and after 30 hours the rate of adsorption became approximately constant, as can be seen from Fig.3.4. The rate of adsorption depends on the humidity, and presumably also on the temperature, though only isothermal studies were made. Samples from three batches of magnesium oxide, two studied soon after preparation, and the third about two years after preparation, showed good correlation with each other in their atmospheric adsorption characteristics. In a study of the adsorption of water on magnesia which had not been reheated after calcining, the two. fresh samples had adsorbed the same quantity of water by the start of the straight-line portion of the adsorption versus tiee isotherm, to within ,,25 of each other, while the stored magnesia had adsorbed about less water at this point than had the other two samples. The magnesia which had been fired to 1000°C. for 1 hour had ads- • orbed about 16S. less water than the as-stored material by the start of the straight portion of the isotherm. The slope of the straight porticn of the isotherm was the same for all the samples to within •t •WATER SORPTION

Sorption of Water Vapour on Magnesium Oxide.

50 100 150 200 TIME (HOURS) - 134 -

4.3%, though the sample fired at 1000°C. adsorbed least quickly. The samples hydrated in an atmosphere with relative humidity about 305.; adsorbed water at about the same rate as those in the atmosphere, though less water had been adsorbed at the start of th::'straight porlivn of the adsorption isotherm. For samples hydrated in an atmosphere of 88% relative humidity, the rate of adsorption was very much faster, being about thirty times the rate of hydration at•50 and 30% relative humidity. The hydration of magnesium oxide powder to which various amounts of binder had been added was studied at 88% mad 305; relative humidity, and the rate of hydration of pressed compacts was also examined. Considerably less than 112% water would be adsorbed during the handling operations involved in compaction, even under extremely humid conditions. Pellets were much less easily hydrated than the powder, and increasing quantities of binder also supp- ressed adsorption, but there was little difference between the adsorption properties of powders and pellets for times of less than 11'2 hours.. Fig.3.5 shows the hydration characteristics of the Pellets and powders at 30% r.h., and Fig. 5.6 shows the characteristics at 88% r.h. Part of the water adsorbed attacked the magnesium oxide to form the hydroxide. The amount of attack can be measured by heating the material to constant weight at 110-120C., or evacuating at room temperature. Both these techniques were used, but for most of the measurements heating at 110'C. for 2 hours was found to be the most convenient method. Samples of magnesium oxide were weiOled and placed in desiccators over water. The samples were reweighed at intervals,'and some of the samples were dried to find the hydroxide content, and then replaced in the desiccators for further hydration. Figs. 3.7(a),(b),(c) show the rate of hydration as a plot of weight of water sorbed vs. time. Comparison of the results shows that there —135 —

0-6 Wt.% FURTHER WATER SORPTI

0.5

O.4

0.3

0.2

Fig. 3.5.

Further Water Sorption at 0.1 30% Relative Humidity.

10 20 30 40 50 TIME IHOURS3 — I 36 —

10 wt.% FURTHE WATER SORPTI 16- Fi a. 3.6. further Water Sorption at 8 0/a_ Relative Humidity. 14 -

12 -

I 0-

8 -

0 •• 0 10 20 30 40 50 TIME (HOURS) SO ../o WATER SORPTION

70"

60'

50'

40'

30' Fig. 3.7(a)

Magnesium Oxide: Water Sorption and Hydration. 20'

10•

100 200 300 r 400 500 TIME CHRS 80 wt.% WATER SORPTION

70'

60'

50'

40.

30" Fig. 3.7(b)

Water Sorption on Magnesi u rn Oxide. 20.

10'

o o 100 300 400 500 200 TIME [H RS 80 wt-% WATER SORPTION

70 -

60-

SO-

40- oo" •

30- Fig. 3.7(c),

Magnesium Oxide : Water Sorption and Hydration. 20-

ibo •260 360 400 500 TIME HRSJ

- 140 -

is a significant difference in results for samDles in containers of differce; shapes, indicating a dependence of hydration rate on the ratio between volume and the external surface area of the sample. Apart from this, the effect of drying the samples at intervals was to reduce the total amount of water adsorbed compared with the undried sample. Smooth curves could be drawn through the points indicating the extent of hydroxide formation. Analysis of the total quantity of water absorbed was carried Go - G out by using the relations of Ch.oun and Deacon .(1964), i.e. oct, - Go - G Go and Coleman and Ford (1964), i.e. log cart, where Co = partial Go quantity of water for complete hydration = 0.4469, G = partial quantity of water adsorbed, t = time. It may be seen from Figs. 3.8(a),-(b), which show plots of the above relations, that the Chown and Deacon relation follows an almost Go-G straight line for up to -60% water absorption ( =d.0.4), while the Go-G Go log vs. t relation is not followed for more than about 10;Z sorption. However, the relations quoted were for hydration rather than for sorption, and though it is interesting to examine the data for correlation between sorption and hydration, it is the extent of hydration which is of most interest. Go-G -- The broken and full lines in Fig. 3.8(c)(i) (7-G"o vs. t) show the analysis for the Chown and Deacon relation for hydration and absorption. The effect of taking out the samples, drying and rehydrating is to shift the second and subsequent hydration points to G2-G higher values of --- than would normally be the case, but comparison Go with uninterrupted absorption lines shows that the effect is insuff- Go-G icient to make the true values follow a Go relationship. 'o G,_G The broken and full lines in Fig. 3.8(c)(ii) vs. t) Go show the analysis for the Coleman and Ford relation for hydration and absorption. The first three points (after the zero point) lie on a straight line, but this does not extrapolate through the zero Go-G point, and the effect of repeated drying is to increase the log 77-- 'o I.o 0

0-8 1.6 loq q,--G S

F q. 3.8(a) 0-6- T-4

-T*

- 4.0

0.2 -24

0 - O SO 100 150 200 TIME 0.1115] :Stilt 3W11 00C OS1 00I OS

1' 1.0

• • • • 0-8- •

• G 0 • Fig. 3.8(cHi • 0.6-

0.4 —

• O.2— 55. ••• .1b

1 50 100 150 TIME [HRS..'

0 ...... ,„ -...... N. N ',.- T•a- NN\ e-G1 '%‘ ••.• scior Gb T-6- N.%

Fig. 3.8(c)(ii)

T•2-

T•o

gle

6- k o so 100 150 2b0 TIME [HRS] - 145 values over their normal values, for the second and subsequent weighings, and hence the true plot would make the extrapolated line even further from the origin. Thus, while this relation appears to describe the intermediate stage of hydration, from A-10-90% hydration, it is not strictly valid as it does not pass through the origin.

(d) Infrared Spectrophotometric4Studies. In.view of the findings of Webster, Jones and Anderson(1965), that different surface conditions of hydroxyl ions existed, and could be characterised by the infra-red spectra, it was considered desirable to examine the spectra of the magnesium oxide used in the sintering experiments in order that the surface conditions night be better known. Webster, Jones and Anderson reported that a ''normal hydrated -1 -1 surface gave bands at 3752 cm and 3610 cm , while newly-formed -1 hydroxyl groups gave a band at 3710 cm , changing after some hours to the "normal hydrated surfaceo. Razouk and Mikhail (1958) -1 reported bands at 3782 cm for natural brucite and prepared magnesium hydroXide, while fresh magnesium hydroxide gave a band at .ad -1 3700 cm . Benesi (1959) reported only a band at 3698 cm for magnesium hydroxide, while Mara and Sutherland (1953) and Hexter and Dows (1956), working on single crystals of brucite, showed a -1 band at 3650 cm when the c-axit of the crystal was not parallel to the beam, and this corresponded to the 0-H stretching frequency. Figs. 3.9(a) and (b) show bands for magnesium oxide heated to 1000°C., and for natural brucite from Unst, Scotland. The brucite -1 -1 shows a band at 3696 cm , and small shoulders at 3650 cm , -1 -1 3630 cm , as well as a small free water band at 1650 cm , while the calcined magnesium oxide shows no bands in either of these regions. .Fig. 3.9(c) shows the infra-red spectrum of precipitated -146-

magnesium oxide dried at 110°C., and stored for several months, and Fig. 3.9(d) shows the spectrum of magnesium oxide (sample 41020) hydrated by placing in water at room temperature for four days, and dried by evaporation under an infra-red lamp. Fig. 3.9(e) shows the infra-red spectrum of magnesium oxide which had adsorbed ,,1.3% water and had been stored for over a year. -1 The peak at 3698 ± 2 cm is not always so pronounced for stored magnesium oxide, as shown in Fig. 3.9(f) for the main batch of material used. Figs. 3.9(g) and (h) show the spectra for the samples of 41020 and the main batch after hydration over water for 3 days, and Figs. 3.9(i) and (j) show the spectra for the samples after evacuation for 3 hours at <1 mm. Hg. Fig. 3.9(k) shows the effect of evac- -uation of the liquid-water hydrated magnesium oxide (from sample 41020, see (d) above) for 3 hours. When there is a small amount of water sorption from the atmosphere, it appears that the originally loosely held water, char- -1 acterised by a broad band at 3600-32C0 cm (Miller and Wilkins, 1952), changes in time to a more tightly held form as hydroxyl ions, -1 characterised by a peak at 3693 * 2 cm , while the free water band -1 at ,4635 cm diminishes in size. This can be seen in Figs. 3.9(1), (f) and (e). The shoulder at 3610 cm-1 in Fib. 3.9(d) was also found in the nujol spectra, and may well not have any significance. The shoulder at 3784 cm 1 is barely detectable above the background, and was only found in one run of the spec cruet. Table 3.10 shows the peaks tn the infra-red spectra of the samples studied. .714 7 - I

Ibi• ob.

$40,101,.

43.1.411.

LA&

(1)1114 • % ;

OOOOOO 100.

Flg. 3.9(0)- (0 FR & QUENCY Icr 4- 2C 3500 3000 . — 1 4 8 —

vapou by drated M30 (wadi

vapour hydrated Mg0 (main batch

Fig. 3.9(0—i

FREQUENCY I 00 00 L -149 —

.4* for fti— lettir (mac uat on

os forft (d)r after evatuat 1 ...... ,_4,

M90 +limier/ a p otr'

Fig. 3.9(1)—(1)

FR iQUENCY 00 4000 35)0 - 150 -

Table 3.10. Infra-red Spectra of Marmesium Oxide and its qydration. Products, s=strong, !qr.-medium, w=weak, sh=shoulder. Material 1Dry Mg0 2Erucite 3696s 3650sh 3630sh 1645sh 3',Ig(OH)o r 3700s 36672 3450-3150m ..1650sh 4g0+H,)0 p3784sh3697s 3642sh 3610sh? 3600-3050s -1645s „.,Storea - 3696s 3669sh - .1g0 3696m 3600-3100m g0 + 3697s 3642m 3600-3100s 1632s 6:water- 3697s 3642m 3600-3100s 1636s vapour 3696sh3666sh 3650-3050s 1634m 6-after_ 3699s 3644w 1628w 7evacuation' 3699s 3642m 3450-3150m 1626m

It Day be seen that in addition to the strong peak at 3698 -1 2 c2 , there is a band corresponding to a stable hydroxyl bond at 3667 2 c2-1 and a band for less stable hydroxyl bonding at -1 3643 It 1 cm-I. Bound water shows a broad band at 3050-3650 cm , 1 while free water gives the expected band-at ,-1638 12 cm . -1 -1 There is virtually no trace of bands at 3752 cm and 3610 cm OlebSter, Jones and Anderson, 1965), or the strong peak at 3782 - c2 1 reported by Razouk and Mikhail. (1958) for brucite and some partially hydrated samples of mapmesiulA oxide. - 151-

CHAPTER 4.

Sintering.

4.1. The Effect of Pressure on Compaction and Fired Density 152

4.2. Methods of Determination of the Kinetics of Sintering 157

4.3. Densification and Shrinkage Relations 163 logLo vs. log t (a)log D0 vs. log t, and (b)d vs. log t. - 152-.

4.1. The Effect of Pressure on Compaction and Fired Density.

Compaction was effected by the movement of a cylindrical steel piston with a flat end down a cylindrical bore, at the other end of which was a small stationary piston. Care was taken to grind the ends flat and symmetrical. This method of compaction produces certain pressing irregularities. Flattened-cone-shaped isobaric waves pass through the powder on compaction, and at low compaction pressures and lower binder concentrations, compacts failed by breaking into two parts: a cone based on the pressing piston, and the remainder. If the die and press are symmetrical, the isobaric waves are symmetrical, with their apices above the centre of the face of the moving piston. Die-wall friction and internal friction prevent the even compaction of a material, and die-wall friction causes the cone-shape of the isobars, and together with internal friction causes the differences in pressure in different parts of the compact. It has been shown by Kingery (1960) that pre3sure differences of a factor of two may arise in compacts with a length/diameter ratio of less than 0.5:1, and as much as a factor of ten for long pellets with this ratio=5:3.

When powder without binder was pressed, the compacts produced were weak, and crumbled on the gentlest handling, and there was sticking of the oxide to the faces of the die. Binders tend to cause even more sticking of the magnesium oxide to the faces of the die, but this may be counteracted by the application of a thin film of hydraulic oil (which was tested for residue on pyrolysis, as were the binders - see Chapter 2) to the faces of the die. Too much or too little oil again leads to sticking.

Series of compacts were pressed at 1-10 tons total pressure (5-50 t.s.i.) with varying quantities of the two binders, beeswax and cetyl alcohol. The compacts were examined, and two series of each were fired at 1400°C. for 24 and 72 hours. Comparative - 153 -

experiments were also performed at other temperatures and times of firing.

The most successful pressing conditions were found to be compaction at 2 tons pressure (10 t.s.i.) using a material prepared by the addition of 20 ml of 2% beeswax binder solution to each 10 g. of magnesium oxide, the carbon tetrachloride being evaporated off before pressing. This gave, after burning out the binder, reasonably strong pellets with a relative density of 44.1 + 0.4%,

While at lower pressures and lower binder concentrations the compacts failed by forming a cone, as described above, at higher pressures the compacts failed by forming discs parallel to the faces of the die, which fell apart before firing, or, more usually, split apart on firing. Because of this tendency of the compacts pressed at higher pressures to split open, the true density, as measured by the mercury displacement hydrometer, was higher than the apparent density obtained from direct measurements with the micrometer screw gauge.

Fig. 4.1 shows the relation between compacting pressure and green (unfired) density.

Fig. 4.2 shows the effect of compacting pressure on the fired density for a 72-hour firing at 1400°C. (The average of two sets).

At higher sintering temperatures, the effect of higher compacting pressure on sintered densities was even more marked, and for a 3-hour firing at 1660°C. a compact pressed at 2 tons densified to 63% theoretical, whereas a pellet pressed at 4 tons densified to nearly 71% theoretical.

The effect may also be represented as a plot of fired density against green density, and Fig. 4.3. shows such a graph for a 2-hour firing at 1550°C. It may be noted that for a range of green density 43-50% theoretical an almost linear DENSE

50 -

F g. 4.1 Effect of Compacting Pressure on Unfired Density. 46-

4 2-

38-

I I I I 1 2 3 5 9 1O TOTAL PRESSURE ITONS1 0/0

DENSE

65--

60 "

55 Fig. 4.2

Effect of Compacting Pressure

gal on Fired Density . [Fired 72hrs,1400°C.]

50—

4 5-- g - ■ 2 3 4 5 - 6 7 8 9 10 TOTAL PRESSURE (TONSI

70-

FIRED DENSITY

%thcor ctical)

INITIAL DENSITY Thcoretical) - 157 - relation is obtained.

When beeswax binder solution was added to the powder and left standing, the solution became darker in colour, indicating that the carbon tetrachloride was being absorbed into the pseudo- crystals of magnesium oxide, leaving the binder only on the outside of the pseudo-crystals. This was confirmed by examination of polished sections of pressed compacts before and after burning out the binder, in which the position of binder between the crushed pseudo-crystals of magnesium oxide could be seen clearly.

4.2. Methods of Determination of the Kinetics of Sintering.

While firing for fixed periods of time at one temperature is useful in the comparison of different materials, pressing conditions, etc., for kinetic measurements it is necessary to know the extent of sintering at different times, and for comparison of results with models the comparison of sintering rates at different temperatures is also required.

There are two methods by which such measurements can be made:

(1)Direct measurement during sintering of compact height or diameter using either a dilatometer or a travelling microscope outside the furnace operating through a window in the furnace wall.

(2)Withdrawal of the compact for measurement, and either replacing the compact for further sintering, or using a series of compacts, each being fired once.

The advantage of the dilatometric and optical observation methods is that the course of shrinkage of a single compact may be observed, and this facilitates the interpretation of the shrinkage behaviour. The main disadvantage is that the methods - 158 - limit the design of the furnaces and the attainable temperatures, so that only the initial stage and the first part of the intermediate stage of sintering can be examined. If sintering involves a single rate process, and if no phase change intervenes, quenching should simply slow the reaction to a negligible rate, and on reheating the reaction should continue as before. Measurements were made to determine whether sintering occurred to the same extent in refired compacts as in compactseft at temperature, as use of a repeated-firing technique would, if valid, have the advantage of following the course of shrinkage of a single compact, as in the continuous-measurement methods, and could be used at higher temperatures to study the intermediate stage of sintering. If the technique were not valid, it would be necessary to carry out a large number of single-firing runs and make allowance for the variability between compacts. It appears that the technique of taking out the compacts, measuring them, and refiring decreases the final bulk density slightly, and was,found that this effect was greater if the bulk density at firSt withdrawal was less than 60% theoretical density. The effect is shown in Fig. 4.4 as a plot of density versus logarithm of time. It may be seen that a straight-line relationship between d and log t did not appear to hold, and this is discussed in detail later.

In view of this apparent effect of the technique on the results, it was decided that the results of such interrupted- firing runs should be checked against those fora large number of single-firing runs of different lengths of time at the same temperature.

The rates of heating and cooling of a compact on being placed in, and withdrawn from, the furnace were determined, x Individual determinations. o Interrupted-firing measurements.

so- FIRED DENSITY'

(74:Ancor- x etleal)'

70 -

Fia. 4.4 Use of Interrupted-tiring and Single-firing Techniques

60-

1.5 0 0-5 1.0 logarithm TIME Cosio(hourr) - 160 - in order to ascertain the length of time spent at intermediate temperatures, at which different sintering kinetics might apply, or a different sintering mechanism predominate. The firing procedure consisted in plunging the cold crucible into the hot-zone of the furnace, which was 10°C. hotter than the intended firing temperature. The power supplied to the furnace was increased by about 5% during the heating-up period, and decreased to the required level a little before the charge reached the intended firing temperature. This ensured that the charge reached the intended firing temperature as soon as possible, and that the charge was at a constant temperature throughout the firing. At the end of a firing, the crucible was quickly removed from the furnace, and allowed to cool in the air. Fig. 4.5 shows the temperature cycle during the firing procedure.

A platinum container, consisting of a wire basket lined with foil, was used in an attempt to bring the charge to temperature more quickly, but this resulted in breaking of the compacts due to uneven thermal expansion, and thus the alumina crucible was generally used.

It was found that freshly prepared magnesium oxide densified at a very much faster rate than magnesium oxide which had been stored for four months or more. The results for fresh magnesium oxide showed such a large variation that it was decided to use a stored, thoroughly mixed batch rather than calcine magnesium oxalate freshly for each few runs. Fig. 4.6 shows the densification of fresh magnesium oxide (specimens 41137-41143) and stored magnesium oxide (specimens 41135,41136) fired at the same temperature. - I 6 I -

1500

1000 HEATING

la cc U cr4( 0 a. X F- 500—

Fig. 4.5

Temperature Cycle during Firing.

• I 2. 3 4 5 6 --- 0 I 2 3 4 5 TIME (MINUTES) 90

4.6 83- Densification on Firing at 1435°C. of Freshly—tired and 411'36 pf Stored Maanesium Oxide.

80e, 41141 .0" FIRED DENSITY. or— At03-•- FRESHLY ..••••"' 75,

(eietheort, stIcal),

e 41140 41142

65-

x41135 o41136

6O STORED

If 1 55" • T-7 O 0.5 1-0 logarithm TIME Llogio(hours) -163-

4.3. Densification and Shrinkage Relations.

Fig. 4.7, apart from giving a striking further illustration of the effect of green density on fired density, shows that a linear relationship between relative density and logarithm of time almost holds for a considerable length of time, though with a tendency towards faster sintering than that given by the d vs. log t relation. The increase in rate is especially marked at a certain point, in this case at 80-90% relative density. This may also be observed from Figs.4.4 and 4.6. In results on the mixed main batch, the scatter of points was appreciable in all the relations tried, and thus after checking the relationship from the interrupted-firing determinations, elementary statistical analysis was used to find the most probable and/or average slope on a plot. It was considered that more meaningful correlations between behaviour at different temperatures would be obtained by comparison of the average of several runs of single-firing determinations than by comparison of single runs of interrupted-firing measurements. The relations examined were: (a)the logarithmic shrinkage relations log t1D vs. log t, Do and log AL vs. log t, where D = diameter, L = length; L

(b) the somilogarithmic densification relation d vs. log t; (c)the relations 15—AD vs. log t, AL vs. log t;

(d) dl vs. t; (e) log d vs. log t and d (f) log vs. logt. 100-d

None of the relations gave a straight line. d vs t was an extremely poor fit, and the increase noted in the d vs. log t plots 90-

Sq. 4, 7 Densification of Magnesium Oxide FIRED. on Firing at 1655°C. DENSITY clotheor: etical)

Unfired densities of pellets: 6--4 4 9 0 3 %theoretical 70 - v—a 47 • 3 6 — al•""4 48 • 84 - 44.04 - *-"'x 4 3 • 1 8 -

4•1

0 l•0F 2.0 logarithm TIME Dogictiffours)1 - 165 - also affected all the other relations. In view of the extensive use of the logarithmic shrinkage relations and the semilogarithmic densification relation in attempts reported in the literature to fit sintering data to models, the results obtained by assuming a fit to these relations for the first part of the intermediate (up to the point of rapid increase in rate noted in the d vs. log t plot) and for the entire.intermediate stage of sintering were examined. A (IL (a) Log -- vs. log t, and log Lo-- vs. log t. 0 These relations were tested for all the temperatures used in the sintering experiments, 1475-1800°C. There was appreciable scatter in the plots, and it was noted that shrinkage in length was faster than diametral shrinkage, which had also been observed in -- vs log t and -- vs. log t plots. LLL 0 o The slopes of the lines between any two points were plotted as a statistical histogram of the number of slopes in a 0.005 slope range against slope. Even increments of the logarithm of time were selected in order that the most probable slope would be indicated by the histogram. The most probable slope was 0.20 ± 0.03 for log 4L vs log t and 0.14 ± 0.02 for log LDr vs. log t from twelve determinations. Examples are shown in Fig. 4.8.

Least-squares analysis gave the slope of log etA vs. log t

A as 0.21 ± 0.03, and that of log -- vs. log t as 0.135 ± 0.03. Do

The errors in both statistical histogram and least squares analysis include differences between different temperatures, but such differences did not vary systematically.

Thus the shrinkage of the compacts is not isotropic, and if 25- No. . -L. of 1700°C. slopes Fi • 4.8(a) vs. log t Slopes. 0.005 slope • range'

15-

10-

•••

•••• ••t : • •••••1

•••• •••••:

• ••••1

•

' - I T • - 0 O• 1 0.2 0•3 SLOPE

No.ot slopeS 1600°C. in 8

0005 slops Fig. 4.8(1)) r01190 Log=AL Vs-log t Slopes. • I •• :

•

.• • • ••••••• • • : . . • r• •

Vol ••••11, 411=11,

1700°C.

im.• • • • •-• ••••••

- • . - • • v 02 0.3 SLOPE -167- the anisotropy applies at smaller shrinkages, as appears to be the case, the results obtained from dilatometric studies of shrinkage must be reconsidered.

(b) d vs. log t.

Least squares analysis of the results of sintering magnesium oxide compacts for different times was conducted, and a comparison was made of the results for different temperatures by use of an Arrhenius activation energy plot. For the purposes of the analysis, the variation from the straight line relationship was ignored, as explained above.

The results for one set of runs are shown in Fig. 4.9., and the Arrhenius plot in Fig. 4.10. reveals a temperature dependence expressed by an activation energy of 23.5 + 1.5 Kcal/mole. This is obtained by using the empirical equation d d' = k dt whence d' = k in t + C (where d' = actual density) and using the temperature dependence k = ko exp (-E/RT), E = activation energy.

A similar set of runs gave an activation energy of 24.6 + 1.5 Kcal/-mole for sintering at 1500-1800°C. A determination at 1435°C also fitted this activation energy.

If only the first part of the intermediate stage of sintering is considered, up to about 75% of theoretical density, then a better fit to a straight line is usually obtained in the d log t plot, and for the two sets of determinations temperature dependencies were expressed by activation energies of 16.2 + 1.0 and 17.1 + 1.0 Kcal/mole.

Thus, if least squares analysis is applied to the intermediate stage of sintering for fine, pure magnesium oxide powder at 1500-1800°C., an apparent activation energy of 24 + 2 Kcal/mole is obtained, which is in reasonable agreement with the activation energy of 27 + 1 Kcal/mole obtained by Brown (1963)for the — I 6 8 —

Fig. 4.9(a) Densification of Magnesia at 1550°C,

90`

FIRED DENSrry

(°/0 thi

62.393 8.703 log t 0 • - " ••' - I T• 0 0 5 1.0 ,115 2.0 Logarithm TIME kogahours).1 -169 —

Fig. 4.9(b) Dinsification cf Maancski at I 600°C.

1,0 T., 6 1.5 2.0 Logarithm TIME t°810(hall — 170 —

Fig. 4.9(c) Densification of Magnesia at 1650°C.

90- FIRED ' DENSITY, (elle th.)

- . - - Logarithm TIME bogihours) — 171 —

Fig. 4.9(c1) Densification of Magnesia at 1700°C.

90-•

F I RED. DENSI

(c), t I))

• • • 0.5 1:5 2.0 Logarithm TIME 103 — I 7 2 —

Fig. 4 .9(4 Densif !cation of Magnesia at I 75CPC.

90- F IRE D' DENSITY 16/e• thr

80- 1

70-

60..4

69.905 16.524 log t

A . . T.5 0 0.5 1.O i S 2.0 Logarithm TIME (logioarsg

-173 —

Fig. 4.9(1) Den si f i cation of Magnesia at 18000C.

90— 0 0 0 Fl RED DENSITY (etoth)- . 0

80-

0 0

70-

60-

77.106 + 19.675 Ion t g g t 15 0 05 I.0 I -S Logarithm TIME Ioc~O ours Fig. 4.10 Arrhenius Plot of Slopes in Fig.49.

*8 49 5-0 5-1 5-2 5.4 5.5 x10 4 RECIPROCAL TEMPERATURE 175 - sintering of active magnesium oxide at 1300-15000C. Similar treatment of the first part of the intermediate stage of sintering reveals an apparent activation energy of 16.6 + 1.6 Kcal/mole, in reasonable agreement with Morgan (1963), who gave activation energies of 12.8 and 18.9 Kcal/mole for two samples of carbonate- derived magnesium oxide, for the initial stage and the first part of the intermediate stage of sintering. The higher value was obtained when binder was used in the preparation of specimens. In view of the lack of any proposed theoretical justification for any of the relations other than the logarithmic shrinkage relation (for the initial stage of sintering), and the semilogarithmic densification relation (for the intermediate stage of sintering), the other relations will not be discussed further, especially as none of the other relations gave a closer fit to the straight line claimed by their proponents than did the d vs. log t relation.

A further example of the relation between bulk density (expressed as per cent theoretical density) and logarithm of time is shown in Fig. 4.11, in which results for a large number of single-firing runs are shown. — 1 7 6 —

Fig 4.11. Characteristic Sintering Curve.

• • • • T•s 0 0.5 20 Logarithm TIME Vogi4hour4 -177 —

CHAPTER 5.

Grain Growth.

5.1. Theoretical Aspects 178 (i) Surface-tension Controlled Grain Growth (ii)Recrystallisation Calculation of Activation Energies

52.. Forms of Grain Growth Observed 182 (a)Needle-shaped Crystals (b)Platelets (c)Liquid Phase Grain Growth (d)The Distribution of Impurity Elements

5.3. Bulk Grain Growth 189 (a)Measurement of Grain Growth on the Surface (b)Measurement of Grain Growth in the Bulk

5.4. Further Grain Growth Phenomena 211 (a)Crystallographic Control of Grain Growth (b)Grain Splitting - 178 -

5.1. Theoretical Aspects. Absolute reaction-rate theory (Glasstone et al.,1941) has been used by Feltham (1957) and others to derive expressions for simple normal grain growth. Equations for recrystallisation and discontinuous grain growth may also be obtained by use of the theory, and are derived below; the effect of alterations in the distribution of the number of sides per grain is also discussed. The rate of growth in both surface-tension controlled grain growth and recrystallisation is determined by the rate of transfer of atoms from one side of the boundary to the other. There is an activation energy, E, associated with this transfer, being the. energy required for an atom to free itself from its ionic environment.. The driving force for recrystallisation is the stored strain energy, which will be considered here to be uniformly distributed throughout the specimen. There is also a counteracting force associated with the curved grain boundary, as the curvature is in the opposite sense to that which provides the driving force for surface-tension controlled grain growth. The frequency of forward atomic jumps, RT -E N = Avagadro's Number F ( Nh) e xiD RT) h = Planck's Constant ' while the frequency of backward jumps, 4--F--) = ( RN forexp-( surface ÷G tension controlled RT grain growth, where ,G = change in free energy on passing from the convex to the concave side of the boundary = 2XV , where Y.= grain boundary energy, V = molar volume, and r = radius of curvature of the grain boundary. E- G+H For recrystallisation F = ( RT ) exp where H = difference 1. between the bulk free energies of strained and recrystallised material, which is constant with respect to grain boundary curvature. For grains larger than a few tens of atomic diameters across,

- 179 -

the convergence or divergence across the grain boundary will be so small (as the boundary width, A , is not more than about 5 atomic diameters), that the rate of growth may be considered as: = A.(r - hence, (i) I =AATT.exp-(m). - exp-q0] for surface-tension controlled grain growth, and (ii) =q-q-exp-4). [1 - exiD(W714)1 for recrystallisation. But 1 " p ) , as G

and 1 - exp(r)'"4 as (G-H) < RT (i) Surface-tension controlled grain growth. RT G (E ) = 2XXV exp- =--Nh RT. exP-`RTI (7) If the distribution of number of sides per grain remains constant during grain growth, as was observed by Feltham (1957) for some metals, then roD (D = grain diameter), and dD ko ,-E, dt = D ex9 RT) hence D- t (D = initial grain size,) D 2 = 2 lc° exP(-4) • o If the case of varying distribution of the number of sides per grain is now considered, two possibilities arise: (a)Decreasing average number of sides, where average radius of D(1+a) curvature, r, is increasing faster than D, 0,er dD ki exe()E thus dt— (11-) - D RT hence D(2+a) (2+a) -E - Do = (2-1-aY k1 exp(—)RT • t (1-a) (b)Increasing average number of sides, D c< r ha thus 'tDd _ -,, -D(1 a) RT D(2-a) (2-a) 2 -E hence - Do = (2-a) k exp(7) • t A special case arises on consideration of a grain with a large number of sides, each of which is growing outward by surface-

-180-

tension controller. grain growth. If there is no grain-growth of the matrix of grains into which such a discontinuous grain is growing, r is constant, and independent of D, and thus TfdD = k3 ez.p(Tf,) - E D- D =k exp( R)•t , if only the growth of the discon- o 3 ' • tinuous grain, and not the average grain growth, is considered.

(ii) iecrystallisation. 1 h (II G) -E -E exp(7y) = [(const.) - 2M 1(i exp . T) - N PT Nhr -13 but r = 2D , ,thus TITdD = kaexpe-Eff ) - 251B 1 exp(.) therefore D - 151)--I-ln(k D - kb) = k exp( I) • t ka RT a a RT If the effect of the counteracting forte due to surface tension is negligible, ka)> kb , E D = exp (TT) • t a The grain growth rates may be modified by the effect of porosity in a manner similar to that suggested by Kingery and Francois (1965). The deductions from reaction rate theory are summarised below. Normal grain growth: Average number of sides per grain decreasing Dn - D n 04.' t exp() n> 2, not necessarily o RT an integer. Average number of sides per grain constant 2 9 -E, D - Do oft exp() Average number of sides per grain increasing m - Dom D oCt exp(-T) 1

Discontinuous grain growth:

D D t expkypE, Recrystallisation: -E D t exp(7) if the surface curvature effect is negligible. N.B. The second term of the left hand side of the first four of these equations disappears if the initial grain size is negligible compared with the final grain size. It will be noted that in normal grain growth variations from -E the equation D2 - Dot oft exp(77) are due to variations from direct proportionality between r and D which give D = f(r), and change the index of D in the final equation. Attempts to reduce 2 2 t' emo(--) will give the final equation to the form D Do De RT meaningless values for the rate constant and the activation energy. This conclusion was also deduced by Comes (1961) for solid state reactions generally, and by Nicholson (1963). Calculation of Activation Energies. Activation energies may be calculated as follows (Nicholson, 1963) E If Dn = n k exp(TaT) t n logD = log nk(exp4)t In a plot of log D vs. log t for any two temperatures Ti°K and T2°K straight parallel lines will be obtained, the logarithmic time intercepts log t1 and log t2 of which will obey the following relation at constant log D 1 E log nk(exp(---RT))ti = log nk(exp(,-;;--,))t, E -E k exp(7)t i =k exp(7,-)t1 2 2 - const. thus at constant D, k exp(ib -182 —

Or in k - E = ln(const.) - in t (ln t = 2.3026 loglot) TRT A plot of In t vs. 1 will have a slope of E.

5.2. Forms of Grain Growth Observed. Micrographic examination of the surface of the sintered specimens, both untreated and after polishing, revealed the formation of grains by several types of growth. The grain growth of the bulk of the compact appeared to occur in two stages, which will be discussed fully later. In addition to this, three types of grain growth occurred at the surface which, together with another observation, are reported below. (a) Needle-shaped crystals. The growth was observed of needle-shaped crystals, usually on the surface, but also sometimes in the bulk of the specimen. A polished section illustrating a typical example of a needle-shaped crystal growing from the surface is shown in Plate .5.1(a). The grey upper half of the photomicrograph is mounting resin. Under crossed nicols anisotropic areas are observed,-especially at the '?root" end of the crystal. The crystals are sometimes curved, and are often pale yellow in colour. The similarity between these crystals and the crystals which form the bulk of the magnesium oxide produced by thermal decomposition of basic magnesium carbonate (some almost circular crystals are also produced) may be observed by comparison of Plate 5.1(a) with Plate 5.1(b), -183—

Plate 5.1(a) 200x Plate 5.1(b) 709x

Specimen 41559 Magnesium oxide obtained by

1800°C. 5•1 hours calcining basic magnesium carbonate. (h) Platelets. Thin transparent isotropic platelets, up to 5 p thick, often rectangular, but also showing other shapes with included angles of 60°, 90°, 120° and 150°, were found in shallow depressions on the surface. It was not possible to examine the crystals by X-ray powder analysis as insufficient crystals could be obtained. However, the crystals were examined by. electron .microbeam probe analysis, and though some difficulties were encountered because of the lack of perfect flatness of the surface, it was possible to ascertain that there was a constant distribution of magnesium present.over the surface including the crystals, and that there was no preferential distribution of silicon or aluminium. Thus it appears that the crystals are magnesium oxide. Examples are shown in Plates 5.2(a) and 5.2(b). - 184 -

Plate 5.2(a) 900x Plate 5.2(b) 825x Specimen 41441 1600°C. 2072 hrs. Specimen 41547 1550°C. 171/2hrs. The -Platelets are often associated with a small area of anisotropic surface material, presumably silicate, as shown in Plates 5.3(a) and 5.3(b).

Plate 5.3(a) 600x Plate 5.3(b) 600x Specimen 4103 1590°C. 47hrs. As Plate 5.3(a) but crossed nicols It would seem most likely that the magnesium- oxide platelets have grown by vapour—phase transport, presumably using water vapour as the carrying vapour. A pellet had been used as a cover for the charFe during several runs at temperatures up to 1800°C. On the surface of this pellet, which showed extensive grain growth, "negative crystal" holes, similar to those reported by Kingery (19600, were observed, and crystals similar to the platelets described above were found _185_ in these holes. The edges of these crystals :rare parallel to slip steps in the surface of the host crystal; indicating that the crystals were aligned with the host crystals. The crystals were also much thicker than the platelets described above and showed growth markings on their surfaces. An example is shown in Plate 54.

900x Cover pellet, heated for several hours at 1800°C. (c) Liquid Phase Grain Growth. Small particles of silica were occasionally observed on the surface of pressed compacts — dust (sand) partibles which had settled on the pressing faces. of the die in the short time between applying the film of oil and assembling the die for pressing. At higher temperatures the silica gave rise to extensive grain growth. Plate 5.5(a) shows the size of the surface grains in a specimen of magnesium oxide heated to 1800°C. for 1/2 hour, while Plate 5.5(b) shows the grain size where a small particle of silica has enhanced grain growth. An interesting phenomenon may be observed on Plate 5.5(b). The original positions of grain boundaries are seen as white lines inside the larger. grains, and it appears that the grains were stable at that size for such a length of time that thermal grooving of the surface occurred to an appreciable extent. 186 -

Plate 5.5(a) 900x Plate 5.5(b) 600x Specimen 41564.1800°C. 30mins. Same specimen. Larger. quantities of silica produced quite extensive local grain growth. An example of this is shown in Plates 5.6(a),(b), and (c). Plate 5.6(a) shows the normal grain size of the specimen near the surface, Plate 5.6(b) shows grain growth where the liquid phase is distributed as a thin film between the particles and at grain corners, and Plate 5.6(c) shows grain growth where the liquid is present in sufficient quantity to surround the grains.

Plate 5.6(a) 200x Specimen 41559 1800°C. 5.1 hours Normal grain growth — 187 —

Plate 5.6(b) 200x 41559 LiQUia phase grain growth.

Plate 5.6(c) 200x 41559 Large quantity of liquid phase.

(d) The Distribution of Impurity ElementA, A Cambridge "Geoscan" electron probe analyser was used to determine the distribution of any impurity elements present. Examination of the unpolished surface revealed that a small quantity of silicon was present (41%), and appeared to be mainly distributed along the grain boundaries of the surface grains. In view of this, it was considered desirable to examine polished surfaces of the fired compacts to determine whether silicon was present at the grain boundaries in the bulk of the compact. No element with an atomic weight higher than that of neon, except magnesilm, was detected, indicating that no other element was present in appreciable quantities, even at the grain boundaries. At the outside surface of the compact, however, small crystals (-45)u) were found either just on the surface, or broken off and embedded in the mounting resin. These cryStals had been noted above the surface of several compacts, usually only a few crystals, - 188 - but in one case, Specimen 41482 (1650°C. for 69 hours), some areas were almost covered by the crystals, as shown in Plate 5.7.

Plate 5.7. 900x Speciaaen 41482 1650°C. 69 hours.

The crystals were examined by electron probe analysis, and found to contain only silicon with less than 5% calcium and a little sulphur &1%) which. may have-been absorbed during the embedding, grinding and polishing operations, In Plate 5.8(a) the broad diffuse white band is the electron backscatter image of the edge of the compact (Specimen 41584), the upper black area of the photograph being the polished surface of the compact, and the lower black area the embedding resin. The horizontal trace is the silicon distribution along the vertical white line (left to right follows top to bottom). Plate 5.8(b) shows the silicon distribution over the area shown in Plate 5.8(a), and contains some scatter, including some preferential scatter at the edge, shown by the broad slightly denser band across the lower part of the photograph. The plates were prepared by photographing the rages on the display screens, which were produced by using a 15 Kv. electron beam with a current of 78 m,pa, -189-

Plate 5.8(a) 1240x Plate 5.8(b) 1240x Specimen 41584, pressed at 20 t.s.i., fired 1750°C. 66 hours. Electron backscatter image Silicon distribution. and linear silicon distribution.

Thus it may be concluded that there is little impurity in the fired compact, and that any silicon impurity appears to have been eliminated to form silica crystals contaminated by calcium and a little sulphur, at the edge of the compact. It also appears that this silica may be responsible for the liquid phase `rain growth observed at the surface for specimens fired at the highest temperatures, as shown in Plates 5.6(a)-(0.

5.3. Bulk Grain Growth. The main difficulty in observing grain growth in the bulk of a compact is that for a small extent of sintering there is insufficient adhesion for the compact to withstand the grinding and polishing stages, with the result that a large amount of pluck-out makes examination of polished surfaces difficult. For this reason it was not possible to determine accurately the bulk grain size of compacts below about 80-85% theoretical density. Observations revealed an unusual form of grain gro'ith, as shown in Plate 5.9. - 190 -

Plate 5.9. 800x Specimen 41202 1635°C. 24 hours.

As it was thought that this might represent a change-over from one form of grain growth to the nornal grain growth found elsewhere on the same polished surface, the outside surface of several compacts was examined. This revealed that surface grain growth occurs - by the growth of small nuclei until they meet, followed by normal grain growth. Two sequences of such growth are shown in Plates 5.10 (a)-(f) and Plates 5.11 (a)-(f). -191—

Plate 5.10(a) 900x Specimen /11453 1600°C. % hour.

Plate 5,10(b) 900x Specimen 41437 1600°C. 1 hour.

Plate 5.10(c) 900x Specimen 41459 1600°C. 4 hours.

Plate 5.10(d) 900x Specimen 41439 1600°C. 5 hours.

• • 4 * • or. • '•• .• • • _ t 1 • 1 i Plate 5.10(e) 900x 1 il)• i ' 11V 4,...., • . 0 . .. Specimen 41463 1 ' 4.41 • • ...„., , , a • :_.,6 a t , 1600°C. 17 hours.

Plate 5.10(f) 670x Specimen 41457 1600°C. 65"2 hours. -192—

• .410. • es •• • • • • • #.•• ; Plate 5.11(a) 900x ,„j„ 4 • :16 Specimen 41566 1800°C. 12 minutes. • • IP •

Plate 5.11(b) 900x Specimen 41563 1800°C. 19 minutes.

Plate 5.11(c) 900x Specimen 41561 1800°C. 1 hour.

Plate 5.11(d) 600x Specimen 41568 1800°C. 1 hour 40 minutes.

Plate 5.11(e) 600x Specimen 41558 1800°C. 2 hours 30 minutes.

Plate 5.11(f) 600x Specimen 41559 1800°C. 5 hours 6 minutes. — 193 —

(a) Measurement of Grain Growth on the Surface. While the measurement of the average grain size of grains which farm an interconnected array, as in normal grain growth, may be performed simply by counting the number of grain boundaries crossing a certain length, and then dividing by a constant to determine the number of grains for that length (Fullman, 1953), the average grain size of grains growing outward from nuclei is more difficult to ascertain. As it Was not possible to follow the growth of a single grain, it was necessary-to take an average value which when taken for several specimens, would lead to a significant correlation. Initially, an estimate was made of the average size of the largest twenty grains observable on the projection-screen of the. Vickers Projection Microscope, at a magnification of 900 diameters. The estimate was made using a sizinggraticule at the focus of the projection eyepiece lens. The estimate Was repeated for five randomly choSen areas for each speCimen. Average estimates were then plotted on log D vesus log t graphs, and an Arrhenius plot was made by plotting the logarithla of the time intercept at constant grain size (log D = 1.0 ) against the reciprocal of the absolute temperature at different temperatures. The'data are shown in Figs.5.l(a)-(e) and Fig. 5.2. The relation D = k t fitted the data with reasonable success, and an activation energy of 75 i. 20 Kcal/mole was obtained from the Arrhenius plot. i.e. exp.(- 75000 R 20000 D = ko' ) t In view of the difficulty of observing the grains by direct projection, it was decided to measure the grain size shown on photographic plates in an attempt to obtain a more accurate grain size determination. Two or three plates of each specimen exhibiting the early grain growth were taken. Mg. LI Grain Size at the Surface of Sintered Specimeni.

(a) ( b I

11750°C. I 11700° C. I

.7m 0 or 0 %m.o.

CC •

• 0—

a O —J

" I 1 • ' ' ▪ I • II •I I II I •15 0.5 1.0 T•S 0 05 1.0 Logarithm TIME io91ethour4 Logarithm TIME ogia(hourii Fig. 5.1 (contd.)

• r. • - I 0 0.5 1-0 1.5 0 0.5 Logarithm TIME 1 (hoursji o TEMPERATURE °C.) 18,00 1750 1700 1650 1600 15;0

1 og t 10

•

0 1O

0 0; 0

Fla. 5. 2 0.0 Arrhenius Plot [Data from Fig.5.11. L.• •

0- ul X

0 -I T-5. - . - - - I — I att 4.9 5.0 51 5.2 53 5.4 5.5 s10-4 RECIPROCAL TEMPERATURE( 1 1 - 197 -

The sizes of all observable grains on the two plates were measured, in order to find the distribution of sizes. Fig. 5.3(a) shows this distribution for one of the plates. It may be observed that most of the grains are very much smaller than the few largest grains. Fig. 5.3(b) shows that the number of grains increases approximately exponentially as the grain size decreases. Comparison with the second plate did not appear to show any great change in the size distribution, and it was therefore considered reasonable to take the average size of the largest fifty grains as a criterion for the comparison of grain sizes in the specimen for different times and temperature of firing. It was observed that the size of grains at the start of normal grain growth was 10-15p. In view of this it was considered that the largest fifty grains on a quarter-plate area (110-83 p at 900x) were those which contributed most to the grain growth. The average sizes coaputed on this basis are shown in Figs. 5.4(a)-(f) as log D vs. log t plots, and the Arrhenius plot to derive the activation energy is shown in Fig. 5.5. Again the relation D = k t appears to be obeyed, and an activation energy of 79 ± 25 Kcal/mole was derived. 25000) i.e. D = ki exp (- 79000 i RT t. After the grains had grown to such an extent that they joined, the grain growth was slower than that represented by the Dot t relation. The average grain size was calculated by taking the number of intercepts of grain boundaries on 5 cm. lines drawn on the projection screen, when the magnification was such as to produce clearly observable grain boundary intercepts - about 3-12 intercepts per 5 cm. Initially the numbers of intercepts at forty random positions were counted ( two mutually perpendicular 5 cm. lines were used), but as it was found that twenty positions gave satisfactory results (within i 2% of the results for forty positions), most of the counts were made with twenty positions per specimen. There was a little -198 —

NUMBER OF GRAINS 1.14 AREA 110p x 83p LOG ( NUMBER OF GRAINS) .0 360'

320

280-

240-

[largest' 50

200.

largest 20

160

120 • ii:rgest 50 SO -

II:rgest 20 40

4 -s- 14; - a. -211?44 GRAIN SIZE

Flo. 5.3. Groin Site Distribution. Fig. 5.4. Grain Size at the Surface of Sintered Specimens (from Plates).

(a) (b) 1750°C. [1700°C. 0

1.0 0 or O

0 I T•5 0 0.5 1-0 T5 0 0•5 Logarithm TI ME 1:110 ( hours)] Fig . 5.4 (contd. )

0 0

P.1 0 O

CC 04 E - oi O O

- - 0 140 1-51f5 0 05 1.0 1.5 Logarithm TIME [Iog io(hours)i Fig. 5.4 .(c ontd.

(e) ( f) 1550°C. 1800°C.

0 O

8 H

411 0 O N 8 0

40 .5 0 CC

0 • hm it r a Log

0 • -C • I T5 0 0 5 1.0 1.5 T5 0 0.5 Logarithm TIM E (2910 hours)1 TEMPERATURE (°C.)

11300 1750 1700 1650 1600 1550 log10 t

1.5-

• 0

Fig .5.5. Arrhenius Plot [Data from Fig. 5.41

•-• 0

T•5 - . - - — 48 49 50 51 52 53 54 55 x 10 RECIPROCAL TEMPERATURE ( I T°K. - 203 - variation in grain, size between the centre and the edge of the face of a compact (larger at the edge), but only in one case (1800°C., 12 hours, Specimen 41560) was the variation greater than ,,10%, and in all cases the average was taken. Fig. 5.6 shows the log D vs. log t plot for this normal grain growth on the surface. It may be seen that while the relation D2 = k t gives a reasonable fit to the data, the best fit is given by D-2.353 = k t. Arrhenius plots, as logarithmic time intercepts at log D = 1.4 vs. 1 are given for both these relations in Fig. 5.7. An activation energy of 115.5 ± 10 Kcal/mole was derived for the D2 = k t relation,. and an activation energy of 124.5 10 Kcal/mole fitted the data for the D2.353 k t relation.

(b) Measurement of Grain Growth in the Bulk,; Polished specimens were obtained in the manner described in Chapter 2, Section 5. Thin sections were also prepared,- butit Was found that the grain size was often so small that the number of grains in the thickness of the specimen made accurate grain size estimates impossible. While thermal etching (exposure to high temperatures for short periods of time) was found by Nicholson (1963) to be the most effective method of revealing grain boundaries in zinc oxide, it was anticipated that the higher temperatures and longer times required for etching magnesium oxide would be difficult to attain in an easily controllable manner, and might lead to further grain growth. A further disadvantage of the technique is the need for demounting the specimen. It was thus decided to attempt to find the most successful chemical etchant. Various dilute acids were used, of which 10% aqueous acetic acid was-one of the most successful, though the longer etching times required led to some attack of the bulk of the grains. The most successful etchant was found to be 20% aqueous sulphuric acid, which not only delineated most of Logarithm GRAIN SIZE 0 Vs O 0 • %

, \ A \\ \\ \ r , ‘, to° \ A\„ 0 \\ '

3 ‘\\ ` \`‘ E \ \ ‘, . • m 0 \ •, • \ P P % ♦ % oluJoN l JO up

up /4a. 41

— 0 —

TEMPERATURE (° C.1 1800 1750 1700 1650 1600 1550

!Ogle!. • _ - eeP k t 2 X Oa•f, D kt

••Ia

r, 1-0- Fig. 5.7.

OM. 4 Arrhenius Plot Data from Fig.5.6k IA x.*.;:: 2 ...,.. 1- 0•5 - .e " sie _ o .. ..- J .\: •

0 . - f - . 443 4.9 50 54 5.2 5.3 54 55 If 1014 RECIPROCAL TEMPERATURE \MCI -206- the grain boundaries, but also created dislocation etch pits, which facilitated differentiation between grains by observation of the different direction and size of the etch pit for different crystallographic orientations of the polished surface. While differentiation may be made between the various grains on Plate 5.12 by observation of the otherwise unbalanced grain edges, the plate nevertheless indicates the manner in which dislocation etch pits can be used to estimate the position of grain boundaries when it is not possible to determine their position by other means.

Plate 5.12. 227x Specinien 41560 1800°C. 12 hours.

It was found that the grains at the edge were, on the average, significantly larger than at the centre, but at higher temperatures and longer times, as the centre grains appeared to grow faster than those at the outside, the grains at the centre on polished specimens became the larger ones. The average grain size was determined as described before, though differentiation was made betleen grains within mm. of the edge and those in the. centre of the compact. The grain growth at the edge of the compact is shown in Fig. 5.8, and the Arrhenius plot (Fig. 5.9) gives an activation energy of 115.5 ez 15 Kcal/mole. The grain growth at the centre of the compact is given in Fig. 5.10, and the Arrhenius plot (Fig. 5.11) gives an activation 2 0-

ul N

Z re 0 1-0 E .a Fig. 5.8. a Bulk Grain Growth at the Edges of Compacts. 0

. • - 0.5 1.0 1.5 2.0 Logarithm TIME cig (boa rs)1 TEMPERATURE (°C.) 1400 17,50 17 DO 1610 1600 1550 logio t

2'0 N X X

Fig. 5.9. I 2 Arrhenius Plot [Data from Fig.5.8.1

I • • 4.8 4.9 51 5.2 5.3 5.4 5.5 s104 RECIPROCAL TEMPERATURE Toot 0 hm it r a Log

r r- 0.5 1-0 Logarithm TIME

TEMPERATURE (°C.) 1650. 1600 1550 1600I 1750 17.00 . 2.5 X ...._ ...... _01227,.. kt log lot. • — Daft k t u"" X 2.0

O J 1 • 5

X •

Fig. 5.11.

• Arrhenius Plot (Data from Fig.5.10.1 0 .5 0.0

0 -4 , 443 4.9 5•0 5.1 5.2 5.3 5.4 5-5 x 10 RECIPROCAL TEMPERATURE 1 T°K -211 -

D1.227= energy of 128.3 15 Kcal/mole. for the found relation k t, and an activation energy of 77.5 f 10 Kcal/mole if the relation 2 D = k t , which is not a good fit, is imposed on the data of only the four highest temperatures.

5.4. Further Grain Growth Phencuena.

(a) Crystallographic Control of Grain Growth. Plate 5.13 shows step formation on surface grains, which corresponds to the different crystallographic directions.

Plate 5.13. - 600x Cover pellet Up to 1300°C.

While the possibility of some of the steps being slip steps (caused by blocks of material sliding over each other) should not be overlooked, it is most probable that the planes of the steps are those of lower surface energy than the average value which would apply if the surface were drawn evenly over the projections. In observation of normal grain growth at the surface, it was noted that in several cases grain boundaries were orientated parallel to the surface markings, or clearly at angles of 30°, 45°, or 60° to the markings, as may be seen in Plates 5.14(a) and (b). — 212 —

Plate 5.14(a) 900x Plate 5.14(b) 400x Specimen 41485, SpeciDen 41534 1?00°C. 24 hours. 1550°C. 66 hours.

A similar observation was made (Plate 5.16) on a polished specimen at the edge of the pellet. The dislocation etch pits give an indication of the crystallographic direction.

Plate 5.15. 400x Specimen 41220 1545°C, 68 hours.

It is suggested that under certain conditions, possibly related to local impurity concentrations, the contribution of decrease in free energy by formation of certain crystallographic faces may be sufficient to override the tendencies for normal surface—tension controlled grain boundary configurations. -213—

(b) Grain Splitting. It further appears that required grain boundary configurations during grain growth are sometimes maintained only by the splitting of an already-formed crystal. Pure displacement may occur, as shown in Plate 5.16(a) and (b), or twist may take place, as shown in Plate 5.17.

Plate 5.1.6(a) 600x Specimen 41499 1700°C. 1 hour.

Plate 5.16(b) 900x Speciaen 41457 1600°C. 651h hours.

Plate 5.17 600x Specimen 41499 1700°C. 1 hour. - 214 -

CKAPTE2 6.

Discussion.

6.1. The Preparation of Pure Magnesium Oxide. 215

6.2. Therm.ogravimetric Analysis of Magnesium Oxide. 217

6.3. The Initial Adsorption of Water Vapour. 21? 6.4. Hydration of Magnesium Oxide. 21? 6.5. Infra-red Spectra of Magnesium Oxide and its Hydration Products. 220 6.6. The Initial Stage of Sintering. 221 6.7. The Intermediate Stage/Final Stage Sintering Model. 223

6.8. Grain Growth during Sintering. 226

6.9. :eliability of the Sintering Data. 227 6.10, Reliability of the Grain Growth Data. 228

6.1 1. Grain Growth Activation Energies. 229 6.12. Conclusions on Sintering and Grain Growth. 231 6.13. Suggestions for Further Research. 231 - 215

6.1. The Preparation of Pure Magnesium Oxide. The main impurities in the magnesium oxide used in the sintering experiments were silicon (nearly 100 ppm, 0.01%), calcium (20 ppm), sodium and potassium (21 ppm and 16 ppm respettively), and aluminium (16 ppm). The limits of detection of most of the transition metals were about 10 ppm each, and it would be advantageous to reduce these by choice of a suitable technique. The use of two magnesium hydroxide precipitations and the elimination of two oxalate head fractions reduced the level of metallic impurities to about 200 ppm, and appeared to give a considerable•reduction in. the concentration of aluminium, and significant reductions in the concentrations of calcium, the transition metals, and zinc, in comparison with the magnesium oxide produced by Brown (1963). It appears from the work of Duff (1966) that the use of polypropylene apparatus reduces the quantity of silica found in the product. However, there was still a considerable silica content in Duff's magnesium oxide, and though careful precipitation of head fractions may reduce this quantity, it is unlikely to eliminate it; it is most probable that the silica is occluded on the surface of the manesium actuate precipitate, but such occlusion does not appear to be sufficiently strong to eliminate silica from the solution by Partial precipitation. It would be advisable to conduct accurate analyses of the distilled water used. If this is found to be a major source of silicon (silica appears to be slightly steam-volatile), then ion- exchange resins could be used to remove it, though contamination by alkali metals, often associated with such resins, must be avoided. Recrystallisation of the magnesium nitrate and ammonium oxalate would contribute to the purification, and should be especially successful in the reduction of the concentration of alkali metal ions. The concentration of calcium in the magnesium nitrate solution -216 - could be reduced by the use of a chelating agent. Care must be taken to select a chelating agent which will not introduce undesirable anions into the final product. EGTA (ethylene glycol bis-p-amino ethyl ether tetra-acetic acid) complexes with calcium to give a much more stable complex than that with magnesium. An extraction procedure has not been described, and it would be necessary to carry out preliminary investigations to find an efficient_ extraction method. Alternatively, recrystallisation of the magnesium nitrate could be carried out with the complex still in solution, and the calcium should then remain in solution during the recrystallisation. Some of the magnesium would also be complexed, and thus more magnesium would be lost than in straightforward recrystallisation. Another coraplexing method of purification could be used to eliminate aluminium and several other metallic ions from the magnesium nitrate solution before recrystallisation. At pH 5, shaking with a dilute solution of 8-hydroxyquinoline in. chloroform or carbon tetrachloride should eliminate aluminium, iron, nickel, cobalt, copper, bismuth and zinc. It would be necessary to ensure that no chloride is introduced into the product by this procedure. The following procedure could therefore be used to obtain a purer product: Using ion-exchange purified distilled water in polypropylene apparatus throughout, follow the procedure outlined below. (1)Allow magnesium to stand in the magnesium nitrate solution in order to deposit less electropositive metals on its surface, as before. (see Section 3.1(b) ). (2)Precipitate magnesium hydroxide by small additions of ammonium hydroxide solution, as before. (3)Acidify to pH 5 and extract with 8-hydroxycuinoline in chloroform or carbon tetrachloride. (4)Add EGTA, and either extract, or leave in solution during recrystallisation of magnesium nitrate. (5)Recrystallise magnesium nitrate. -217 -

(6)Recrystallise ammonium oxalate. (7)Take magnesium oxalate head fractions of both magnesium nitrate and ammonium oxalate solutions, as before. Then precipitate, calcine and analyse, as before.

6.2. Thermogravimetric Analysis of Magnesium Oxalate. The possibility of a transitional intermediate carbonate in the decomposition of magnesium oxalate was discussed in Section 3.1(c). Further work, including examination of the effluent gases during the course of the decomposition, is required to clarify the position.

6.3. The Initial Adsorption of Water Vapour. The initial adsorption. of water vapour appears to occur very fast, and is controlled by the rate at which water molecules can diffuse to the adsorbing surface. The medium of diffusion is most probably the vapour phase, but the contribution of surface diffusion may be high where constrictions impede the passage of vapour-borne molecules, but allow the effectively more concentrated surface- adsorbed molecules, travelling in the physisorbed second layer `of water, to reach fresh surface.

6.4. Hydration of Magnesium Oxide. The rate at which magnesium oxide is hydrated on exposure to moist sir may be determined either (a) by using a sim;le sample, and determining the degree of hydration after an interval of time, and then rehydrating, as in the work described in this thesis, or (b) by using. a number of samples to determine tie decree of hydration after different intervals of time. The disadvantage of the single sample technique, (a), is that it is necessary to evaporate off the physisorbed water in order to determine the degree of hydration, and this disturbs the hydration process, because this water must be replaced before the hydration - 21E3 - can continue at the original rate; as this takes sonic time to accomplish, during which time the hydration has presumably been proceeding at a lower rate, the effect of the disturbance is difficult to estimate. The disadvantage of the use of several samples (technique (b)) is that there is such a variation between the hydration rates of different samples that a lare number of samples would be required for unequivocal confirmation of a rate theory. It has been shown that qualitative correction for the disturb- ances incurred in technique (a) indicate that neither the relation proposed by Chown and Deacon (1964) nor that proposed by Coleman and Ford (1964) could be confirmed. This conclusion is not entirely unexpected. Both the proposed relations claimed to consider the rate of hydration (---dx d t) to be proportional to the concentration of unreacted magnesium oxide (x) i.e. a first order reaction. dx dx kx , thus -7 = kdt In = kt const.

As x = quantity of magnesium oxide remaining, x = const.(207G --)G Go ' where Go = partial quantity of water for complete hydration = 0.4469, G = partial quantity of water adsorbed, thus log (--"tz.-) t . lo Go Thus the relation of Coleman and Ford is the correct representation of a first-order reaction. However, the first-order reaction relation is applicable only when there is an equal probability of any molecule in a volume containing the reacting substance (usually a gas or solution) reacting either on its own or with another reagent which is distributed evenly throughout the volume. Thus the relation should apply to the hydration of magnesium oxide only if the water molecules are able to travel throughout the volume of the magnesium oxide, and if the magnesium oxide reacts with the water evenly throughout the volume. For these conditions to apply it would be necessary for the mean free path of the water molecules to be comparable with, -219- or greater than, the dimensions of the specimen. The packing of the magnesium oxide does not permit such ubiquity, and thus attack must be at the surface of the magnesium oxide. Under such circumstances, there are three possible modes of control of the reaction. (1)Reaction-control by the rate at which water attacks freshly revealed surface. (2) Reaction-control by the rate at which newly- formed magnesium hydroxide is transferred into its new lattice, allowing attack of the magnesium oxide below. (3) Reaction-control by the rate at which water can diffuse to the unreacted magnesium oxide surface. Case (1) does not appear to apply as it was observed that in the initial adsorption of water on the fresh magnesium oxide surface control appeared to be effected by the rate at which water could diffuse to the surface. In case (2) the. rate of reaction should be directly dependent on the surface area being attacked, while in case (3) this will be modified by the requirement for the water molecules to diffuse an increasing distance through the magnesium hydroxide to the magnesium oxide surface. It has been suggested (Coleman and Ford, 19:S4) that certain surfaces are more easily attacked than others, namely those at the sides of micropores. It is indeed likely that capillary condensation in such micropores will lead to a higher local water concentration, and this in turn will lead to a faster attack. Considering only the micropore surfaces, and assuming their geometry is not radically changed by the expansion of the lattice from that of magnesium oxide to that of magnesium hydroxide, it would appear that if case (2)were operative, a continuously increasing hydration rate should be observed, as the area of attack, for curved faces, on magnesium oxide is steadily increasing as attack proceeds. However, if case (3), i.e, diffusion to the reacting surface, were rate-controlling, the effect of increasing diffusion distance might well outweigh - 220 -

the effect of increasing area for diffusion, especially when it is considered that water must first diffuse through the first layer of magneSium hydroxide at the surface of. the micropore. This would lead to a decrease in the actual rate of hydration as the reaction proceeds, 0 G and this may fortuitously coincide with a lo7( a--) vs. t relation Go at some stage in the reaction. Indeed a fit to the relation was found for 10..90% hydration,- though the disturbance effect mentioned above might have given rise to an uncharacteristic relationship. Thus it appears that diffusion of water from a micropore through the layer of magnesium hydroxide to the magnesium oxide surface is most likely to be the rate-determining step in a surface reaction which is not expected to bear a simple relation to the concentration of unreacted magnesium oxide. Confirmation of the suggested role of micropores in the hydration of magnesia could be obtained by electron micrographic studies, at high magnification, of the product at various extents of hydration.

6.5. Infra-red Spectra of Magnesium Oxide and its Hydration Products. -1 It has been shown that a strong peak at 3698 4- 2 cm characterised hydroxyl bonding in magnesium hydroxide or hydrated magnesium oxide. This is contrary to the findings of Webster, Jones and Anderson (1965) who found, for less than a mcnolayer of water adsorbed, -1 -1 bands at 3752 cm and 3610 cm , and only a metastable structure with -1 a band at 3710 cm . It is possible that the metastable hydrated product obtained by Webster, Jones and. Anderson corresponds to the product normally obtained by hydration of magnesium oxide, and that the hydroxyls formed break up into small groups of five or six pairs. Webster et al, considered that the protons were closer to each other in the metastable form. If the protons of the hydroxyls at the edge of the group in the "normal hydrated surface" were sited preferentially outward, this would increase the proton-proton distance over that in the metastable surface case, thus lessening the effect of .a proton -221 -

on neighbouring hydroxyl bonds, and increasing the infra-red frequency associated with that bond. -1 This would thus account for the shift of the band to 3752 cm -1 but does not explain the appearance of a band at 3610 cm at the -1 same time. . The band at 3610 cm appears to be associated with. a slightly weakened bond. There are several ways in which such a weak- ening might. come about; thus, if the hydroxyl groups were preferentially pinned at a step or dislocation in the surface, the topological arrangement might lead to an interaction of a proton with a neighbouring hydroxyl bond characteristic of the siting of such groups at the steps or dislocations. Alternatively, association with further molecules of Water above the centre of the groups would give rise to weakened hydroxyl bonds, and thus lower characteristic frequencies. In the case of the magnesium oxide used in the studies reported -1 in this thesis, the shifts to lower frequencies (3667 2 cm and 1 36'+3 i 1 cm ) are fairly small. They are probably associated with topological arrangements characteristic of the material, and it is suggested that they may both correspond to proton interaction in capillary condensed water vapour. There appears to be slightly more interaction for hydrated magnesium oxide immediately after hydration than for the more stable configuration adopted on storage. The differences, while small, are sufficient to provide interest from the theoretical standpoint. Further investigations on magnesium oxide derived from other sources, Provided that the nature of the material is determined by electron microscopic examination, should lead to a better understanding of the interactions.

6.6,The Initial Stage of Sintering. It was found that the shrinkage was not isotropic, indeed, the slopes of the log--AL vs. log t plots (0.21 * 0.03) varied appreciably Lo AD from those of the log—Do vs. log t plots (0.135 4: 0.03). In view of -222 -

this anisotropy, presumably due to pressing effects, it is essential that any future work on the fitting of the data for initial stage sintering to a model should include experiments to determine whether this shrinkage anisotropy is present, and such work should be carried on more than one material to avoid fortuitous correlation of data with the theory. This effect must be borne in mind especially when arbitrary, though explainable, corrections are made to the data to fit theoretical curves. The anisotropy could be eliminated by hydrostatically pressing powder contained in a rubber bag in oil in a press, and machining samples from the resulting compact. However, removing the anisotropy does not render results obtained from logarithmic shrinkage-time plots more valid in the direct interpretation of the slopes of these plots in terms of grain-boundary or volume diffusion. It would be appropiate at this stage in the development of sintering theory to use graphical or statistical methods to determine the shrinkage behaviour of a compact consisting of a random array of particles of the shape deterMined by electron microscopical examination of the material under consideration. This could be facilitated by use of a monodisperse array of regularly shaped particles, and it is. suggested that thermal decomposition of oxalates under shock-heating conditions, with the resulting fine powder collected by electrostatic dust precipitation, might. provide a good sample for investigation. It would then be instructive to compare results obtained by use of such a material with those obtained by use of a much coarser material, though it is essential to ensure that the coarser material is as pure as the oxalate-derived material. The model under consideration for an oxalate-derived monodisperse magnesium oxide sample would consist of right-angle edges, and cube corners on a plate of varying orientations. One of the difficulties in the application of such model systems to the small particles obtained by the thermal decomposition of -223 - salts is that even loo shrinkage may correspond to no more than twenty atomic layers being added at the neck, and the use of smooth lines to describe such a process, including the grain boundary groove which is needed to balance solid-vapour and grain boundary tensions, becomes questionable. While the neck area is expected to fill up evenly, it is possible that the normal solid-vapour and grain boundary tension values are not applicable during the building up of the first few atomic layers, and this will affect the model. The model would also be affected if the first few atomic layers were transferred by surface diffusion, causing neck growth without shrinkage. In the experiments described in this thesis, an increase in bulk density from 44% theoretical to )52% theoretical occurred within a very short time of reaching sintering temperature, or perhaps even during the heating up to temperature. Thus the initial stage of sintering was completed before the measurements began. Never- theless, it is interesting to note the correlation between the logarithmic length shrinkage/ time slope obtained in these experiments (0.21 * 0.03) and that of the later sintering of one of the beryllium oxide samples studied by Aitken (1960) (--,0.2).

6.7. The Intermediate Stage/ Final Stage Sintering Model, The model presented by Coble (1961) for the intermediate stage and final stage of sintering is the most promising in its application to sintering data, particularly in its explanation of the semilogarithmic densification relation reported by several workers. However, errors in Coble's analysis should not be overlooked. 1)The dependence of the derived sintering activation energy on the activation energies of both diffusion and grain growth, reported by Morgan (1963), and not on the diffusion activation energy alone. 2)The analysis of the shrinkage during the closed-pore stage. Coble considered that the 24 four-grain corners were occupied - 224 - ny pores, and that the flux from these might be represented as for diffusion between concentric spherical shells. The flux equation is then: -) vacancies/second, J = 4rDv AC(4- d-r 116. where r,d are the inner and outer radii respectively. If the pores are small compared with the diffusion distance i.e. r< d then J = 4rD &Cr . As the pore radius is then rate- v controlling, the topology of diffusion, in this case to grain boundaries rather than the, outer diffusion shell, is considered unimport- ant, and thus the volume flow per polyhedron is given as dV = AC a 3r dt 6J = 2L1Dv o 3 But AC = (2CoYa03 / kTr) and -D = DvQ0 ao (there are printing errors in Coble's paper on these relations), and thus

•. dV _ 48/0 -ea03 dt - kT and as jdV = 6.4rr31, then r3 = 61)Ya.,3(tf—t) 3 ' kT and P = Grf'D X a (t,-t) , which is very close to the open-pore 77L1)kT I stage densification relation for bulk diffusion: P„ 10 DXaQ3(tf-t) likT However, it was claimed that the same analysis applied to the 3 general case, where dV 241rDITYC0 an r.d gave dt T kTr (d-r) (should be 48) 3 4 r r 3D3' a03 t kT It is difficult to determine how this expression was derived. As ,( 4 3) 48-01Nov / a03 fdV=6(1±Trr3T as before, o --Trr = d dt 3 Jr 3 / kT (d-r) If d and r are considered to be independent of time, then

-225—

3 6 (- r ) an t 3 kT whence r3 - r'= 6DXt d kT As P = irr3 PI-2' 13 (1-E) 6DWt 4213 it d kT 6,,rDYt f2 13 (1-r.; Taking d = = 342 P (1-,r) varies from 0.289 at P = 0.10 Iv to 0.584 at P = 0.02, to 0.846 at P = 0.001. Thus if the change from open channel to closed-pore sintering occurred at a little below 10% porosity, and if the models were correct, the sintering could be described by a change-over from one to the other, followed by a reduction in rate (by a factor of two on densifying to 2% porosity), as predicted by Coble (1961). This examination of the analysis has been instructive in indicating the effect of the diffusion distance on the sintering relation even at porosities as low as 0.1 %. Further, however, r and d are time-dependent, and thus it is not possible to ignore them in the integration with respect to time. While the derived expression may approximate the solution when the time-dependencies of r and d are considered (the expression is correct at the limit the variation from the true solution. will be both time and temperature dependent, as the value 'of d, the diffusion distance, is governed by the grain .growth laws. A true solution of this problem could be found by considering the shrinkage of pores by diffusion of vacancies from the progressively decreasing pore surface, but - as assumptions made by Coble require the pores all to be of even size and placed at the four- grain corners of the polyhedra, and this is not observed on photomicrographs, further analysis would be required to determine the effect on the model of variation of pore size, diffusion distance, - 226 - and pcsitioning of pores away from grain corners, In summary, the closed-pore stage of si:t:r=ban:ot be described rigidly by a simple relation such as as more care is required in the integration of the differential equations which lead to such a relation. Thus, while a decrease in rate from that which prevails at the intermediate stage may be expected during the final stage of sintering, it will probably not fit such a relation.

6.8. Grain Growth during Sintering. It has already been observed that the sintering of magnesia powder of small particle size does not follow the d e< log t relationship predicted by Coble for the intermediate stage of sintering. Instead, a sigmoi.dal sintering curve is produced on the d vs. log t plot. The enhancement of sintering (see Fig. 4.11) is most pronounced at about the time of the changeover from the initial form of grain growth (characterised by D.0

6.9. Reliability of the Sintering Data. Apart from the variation from the straight line relationship in the semilogarithmic densification plot, towards the sigraoidal curve, there is considerable scatter in the data, which is difficult to account for. Considerable care was taken to ensure consistency in the preparation of specimens and the firing procedure. It is unlikely that there is such a variation in the impurity content from one specimen to another as would cause the observed scatter in the data. The magnesium oxide was very thoroughly mixed and it is not easy to visualise how any local variations in impurity distribution could affect the densification of the entire compact. It is recognised that the water vapour pressure in the furnace hot zone was higher than that in the ambient atmosphere, owing to the dehydration -228— of the specimen and the ceramics used, and to the diffusion of hydrogen through the work-tube into the hot zone. The water vapour pressure presumably varied somewhat from run to run. However, it is not expected that the densification of magnesium oxide would be greatly affected by minor changes in the water vapour oressure. It is probable that some transport of magnesium oxide occurs by an evaporation-condensation process with magnesium hydroxide transport through the vapour phase, but it is improbable that variation in the water vapour pressure could cause large variations in the fired densities of sintered compacts. In view of the lack of an explanation for the scatter in the data, separate sets of data on the same batch of magnesium oxide, at the same temperature, were compared. While it is recognised that the minimum of data were available for more than tentative quantitative deductions by the use of elementary statistical analysis, it is interesting that good correlation was found between the two sets of data, and between both sets of data and the findings of Brown (1963) for the intermediate ctae of sintering and Morgan (1963) for the initial stage and first part of the intermediate stage of sintering.

6.10. Reliability of the Grain Growth Data. The linear relation between the logarithi of the number of grains of a particular size and the grain size is assumed to have constant slope in order that the average size of the largest twenty or largest fifty grains should have any significance. While this appeared to be true for two plates taken at different sintering times and temperatures, it would be necessary for the constancy of this relation to be confirmed before more than very tentative quantitative deductions can be made. The accuracy of the sizing of the grains is probably impaired by the low contrast between the grains and the background at that stage in the grain growth. If further - 229 - measurements were required it would be advisable to obtain high contrast enlarged prints from such plates. The apparent activation energy for the initial grain growth, obtained by use of the average size of the twenty largest grains on each of five areas viewed on the projection screen of the microscope, was 75 + 20 Kcal/mole. Use of the average of the fifty largest grains observed on the photographic plates gave 79 t 25 Kcal/mole. In both cases, however, a curve of the same shape (slop, decreasing from left to right in Figs. 5.2 and 5.5) would fit the data better than the conventional straight-line Arrhenius plot. This curvature was not observable in the Arrheniu6 plots on normal grain growth, and may be due to the particle size distribution effect.. For grain growth on the surface, an activation energy of 2.353 124.5 t 10 Kcal/mole was derived for the D = kt relation which best fitted the data, and enforcement of the D- = kt relation gave an activation energy of 115.5 1.0 Kcal/mole. For bulk grain growth, measurement of grain sizes at the edge of the compacts indicated the relation D2 = kt to be applicable, and an activation energy of 115.5 i 15 Kcal/mole was derived. Measurement of the grain sizes at the centres of compacts gave 1.227 the relationship D = kt, and an activation energy of 128.3 15 Kcal/mole. However, the Arrhenius plot has the appearance of two straight lines separated by a kink, and this is especially notice- 2 able when the D = kt relation, which is not a good fit, is imposed on the data. The lines appear to show an activation energy of 77.5 ± 10 Kcal /mole,

6.11. Grain Growth Activation Energies. It may be seen that two ranges of activation energies for grain growth, 120 ± 20 Kcal/mole (for normal grain growth), and 77 + 20 Kcal/mole (for initial grain growth and possibly for normal grain growth) have been derived. It is quite contrary to the present - 230 -

theory of grain growth that two different activation energies should exist for different forms of grain growth in the same solid. Further, the grain growth activation energy would, from the theory, be expected to be comparable with the grain boundary diffusion activation energy of the slowest ion. While the grain boundary diffusion activation energies for magnesium and oxygen ions in magnesium oxide are not known, it is expected that they are considerably less than the bulk diffusion activation energies. While the activation energy for initial grain growth (77 i 20 Kcal/mole) is closely comparable with that of bulk diffusion of magnesium ions in magnesium oxide (79 Kcal/mole; Lindner and Parfitt, 1957), it also includes the activation energy of oxygen ion bulk diffusion (62.4 Kcal/mole; Oishi and Kingery, 1960b) in its limits. The diffusion coefficients given indicate that oxygen ions should be slower-moving (and hence rate-controlling) in magnesium oxide by 2 a factor of --10 at the temperatures used. It is conceivable that the faster diffusion of magnesium ions could cause a charge gradient across a grain boundary, enhancing oxygen ion diffusion. However, it would not seem plausible that this could occur to such an extent as to make magnesium ion bulk diffusion rate-controlling (with an activation energy of 79 Kcal/ mole). Clare (1966) noted that the apparent diffusion activation energy in initial stage sintering of beryllium oxide was 138 Kcal;' mole. The reported values for the oxygen ion bulk diffusion activation energy for beryllium oxide are between 36 and 92 Kcal/mole, while the activation energy for grain growth, 104 Kcal/;dole, is within the range of values given for the bulk diffusion of beryllium in beryllium oxide, 63-114 Kcal/mole. The large range of values given for these diffusion activation energies suggests that perhaps not too much reliability should be attached to the reported values for magnesium and oxygen ion diffusion in magnesium oxide until confirmatory studies have been made. -231 -

6.12. Conclusions on Sintering and Grain Growth. Thus it may be concluded from this work that normal grain growth occurs after an initial form of grain growth, probably dis- growth, continuous grain/in the sintering of very fine magnesium oxide powder. The normal grain growth follows a relation Dn = kt, where n is close to 2, and k is temperature dependent, corresponding to an activation energy of 120 i 20 Kcal/mole. This value for the grain growth activation energy is comparable with the non-liquid-phase grain growth activation energies of 104 -4- 20 Kcal/mole (for D3 = kt) and 146 ± 25 Kcal/mole (for D4 = kt) found by Nicholson (1963) for magnesium oxide doped with titanium oxide and iron oxide, respectively. The semilogarithmic relation for densification is not obeyed, most probably because the prerequisite of a D3 = kt concurrent grain growth law is not foUnd. Hydration. during preparation of specimens was insufficient to cause widespread modification of the lattice on desorption, though local modification may have taken place. "Active" metal oxides become less active with time. In view of the reduced affinity towards water vapour it is probable that a slow reduction of surface area by surface diffusion into micropores occurs on "ageing". However, it would be difficult to explain the great decrease in sintering rate by this single phenomenon. It is possible that on ageing an equilibration reaction occurs, forming a stronger and more stable electrical double layer (preferential oxygen siting) on the surface, which hinders subsequent diffusion and sintering.

6.1 . Suggestions for Further Research. (1.) Firstly it would be of great value to obtain accurate grain growth measurements in fully dense pure magnesium oxide. Though such magnesium oxide could be prepared by quenching a melt, the -232 -

risk of contamination at such temperatures (2850°C.) is so high that it Would be more advisable to obtain pure dense magnesia by hot- pressing pure magnesiUm oxide, and then studying the grain growth. Such a densification process would probably produce magnesium oxide. with grain growth advanced into th.e normal grain growth stage, with Minimum grain sizes of ',Up. Any modification of the grain growth relations by crystallographic control Of grain growth should be examined, and variation in the. distribution of the number of sides per grain with firing time and temperature should be investigated. (2)Further observations should be made of the initial stage of grain growth, both qualitatively, using electron Microscopic examination of fractured and untreated outside surfaces, in order to determine the fine structure of the boundary between the growing grain and the matrix, and quantitatively, in further examination of the grain size distribution and its variation with time and temperature, if any, and interpretation of the grain growth rates in the light of the knowledge of such distributions. (3)Examination of "active" metal oxides to determine the cause of "ageing". Electron microscopic examination, at high magnification, of an "active" metal oxide at intervals after preparation should provide new information. (4)In addition to these, further data on the ionic diffusion activation energies, both in the bulk and along grain boundaries, are required for the sintering and grain growth processes to be better understood. The production of the platelets of magnesium oxide by vapour transport may be of use in th.e preparation of small pure single crystals:; - 233

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ACKNOWLEDGEMENTS.

I wish to thank my supervisor, Dr. A.J.E. Welch, for his advice and guidance throughout this work, which has been greatly appreciated.

The work was made possible by a generous bursary awarded by the Steetley Magnesite Company, and I should like to thank Dr. W.C.

Gilpin and the staff of the Steetley Organisation Research Department for the interest they have shown.

Thanks are due to the E.M.I. Materials Application Division, who took the electron photomicrographs of pure magnesium oxide.

I thank Dr. J. Gavrilovie' of the Mineral Technology Department,

Imperial College, for his work on the electron microprobe analysis.

Much of the work on the preparation. and analysis of pure magnesium oxide was done in collaboration with E.J. Duff, who needed similar material for other work.

I extend my thanks to all those in the Chemistry Department who have provided both access to apparatus and helpful discussions.

I thank my wife for her - help in typing and in the preparation of the photographic prints.